COMSOL News 2004 · The focus of this fi rst issue of COMSOL News is multiphysics modeling. Consider that a typical problem in the area of MEMS (microelectromechanical systems) requires

C O M S O L N E W S V O L . 1 2 0 0 4 1

COMSOLNEWS

V O L . 1 2 0 0 4www.comsol.com

A T E C H N I C A L C O M P U T I N G M A G A Z I N E

Unraveling a Benchmark Study TIPS & TRICKS

>> Filtration SystemsMultiphysics software speeds analysis ofnext-generation filtration systems

>> Fiber OpticsFEMLAB simulations rampup design of processorsfor fiber optics

>> High-Power MicrowavesSimulations key to non-lethalmicrowave weapon

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PRODUCT NEWS

FILTRATION SYSTEMS

Multiphysics software speeds

analysis of next-generation

fi ltration systems

USER REVIEW

A close up on FEMLAB for

soil-sensor design

FIBER OPTICS

FEMLAB simulations ramp up design

of processors for fi ber optics

TIPS & TRICKS

HIGH-POWER MICROWAVES

Simulations key to non-lethal

microwave weapon

UPCOMING EVENTS

UNRAVELING A BENCHMARK STUDY

A PROFESSOR´S DREAM FULFILLED

www.comsol.com

Dear Reader,

Welcome to COMSOL News—a magazine about technical computing. Our goal is to provide you with details on innovative FEMLAB applications, share some of the engineering know-how behind the applications, and convey news about recently developed products and upcoming events.

The focus of this fi rst issue of COMSOL News is multiphysics modeling. Consider that a typical problem in the area of MEMS (microelectromechanical systems) requires analyzing several interconnected phenomena that interact in nonlinear ways (for example, thermal strains, fl uid fl ow, and electromagnetic forces). Multiphysics problems long regarded as too complex for everyday modeling now can be addressed with speed and accuracy, at reasonable prices, and on a laptop.

In this issue we report on several multiphysics projects that demonstrate interesting modeling approaches with broad range promise. In the Fleetguard example, a number of engineers, through sharing of ideas and methods, develop new FEMLAB modeling techniques that dramatically lower the costs of producing and testing fi lters designed to reduce car engine exhaust. The Enablence story describes how simulations are used to optimize the design of photonics processors that will push vastly increased quantities of information through fi ber optics networks. The last case study in this issue is from SARA. Researchers there use FEMLAB simulations in a clever design to disrupt enemy electronic devices with high-power microwave pulses.

As a FEMLAB user you may fi nd more to interest you in the magazine. I am particularly enthusiastic about the section of Tips & Tricks that will make your modeling even better. Do not miss the Product News. Here Lars Langemyr, the VP of Development, unveils the FEMLAB Multiphysics Viewer—a new free of charge product. Send the viewer to colleagues and clients so that they can view and postprocess any FEMLAB model! Of very special interest is an article from long time user Prof. Bruce Finlayson from the University of Washington. In the article Prof. Finlayson chronicles how his interest in FEMLAB developed and how the easy-to-use software changed the way his students learn.

Finally, I want to give you advance notice of the FEMLAB Conferences to be held in Europe and the United States in 2005. These conferences are wonderful opportunities for you to present your work, explore new technologies, and exchange ideas with an interdisciplinary group of modelers and COMSOL developers who are working with and improving the same code you use.

I hope you enjoy this issue of COMSOL News! We want this magazine to be useful to you, and we encourage your comments. You can reach me at [email protected].

© Copyright 2004 by COMSOL, Inc. All rights reserved. No part of this document may be photocopied or reproduced in any form without consent from COMSOL Inc. FEMLAB is a registered trademark of COMSOL AB. MATLAB and Simulink are registered trademarks of The MathWorks, Inc. SolidWorks® is a registered trademark of SolidWorks Corporation. Other product or brand names are trademarks or registered trademarks of their respective holders.

COMSOL NEWS EDITORS:

Best regards,

Leigh SoutterCHIEF EDITOR

Ed Fontes Lars LangemyrBernt NilssonTim NiuMagnus Ringh

Niklas Rom Paul Schreier Almut SeyderhelmLeigh Soutter

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LAYOUT: Stiby & Stiby AB

We welcome your comments on COMSOL News—contact us at [email protected].


P r o d u c t N e w s P r o d u c t N e w s P r o d u c t N e w s P r o d

The development team at COMSOL redesigned the FEMLAB modeling package, from head to toe, to produce the version 3 product family. We used the latest solvers and technologies to make FEMLAB modeling far faster and more memory effi cient than earlier versions. The Chemical Engineering Module, the Electromagnetics Module and the Structural Mechanics Module all capitalize on the up-to-the-minute engine. Included are brand new interfaces, model libraries, and analyses for each application area. This is just the beginning. With FEMLAB 3 technology as the foundation, we are creating exciting new software packages

and adding powerful features to existing products—all integrated into our unique multiphysics modeling environment. The latest additions to the new product line are FEMLAB 3.0a for Macintosh OS X v10.3 Panther and the FEMLAB Multiphysics Viewer.

FEMLAB 3—The Foundation for the Future of Multiphysics Modeling

Explore FEMLAB Models Using the New Multiphysics ViewerThe FEMLAB Multiphysics Viewer is a new software tool for exploring and postprocessing FEMLAB models. The Multiphysics Viewer provides the opportunity for anyone to open, explore, and postprocess a FEMLAB model. Plus the viewer is free of charge. With the Multiphysics Viewer you get access to the powerful interactive environment for postprocessing and visualization in FEMLAB 3.0a. You can freely plot and investigate FEMLAB models with the same features and functionality as in FEMLAB, even the ability to visualize almost any expression that you key in. The variety of advanced graphics options available includes cross-section plots and time-evolution plots over subsections, points, lines, and planes that you defi ne interactively.

> MULTIPHYSICS VIEWERKEY FEATURES

• Open and explore any FEMLAB 3.0 or 3.0a model

• Interactive plotting of model variables and properties using the following plot types: slices, isosurfaces, contours, streamlines, deformed shapes, height, boundaries, and arrows (vector fi elds)

• Animation using AVI and QuickTime movie formats

• Integration along boundaries and subdomains

• Cross-section and domain plots for projection of solution variables along surfaces and lines

• Access to all inputs, preprocessing and solver settings for full review of the models

• Tutorial and selected models included

FEMLAB 3.0a Brings Advanced Multiphysics Modeling to the Mac >

3.0a. You can freely models with the same features and functionality as

, even the ability to visualize almost any expression that you key in. The variety of advanced graphics options available includes cross-section plots

FEMLAB is now available for Apple’s Mac OS X v10.3 Panther. This means that the Macintosh community can benefi t from powerful FEMLAB 3 simulation and exchange models with the community of users working on other major platforms, including Microsoft Windows, Linux, Solaris, and HP-UX. FEMLAB 3.0a is the fi rst native Macintosh version of a scientifi c software package for multiphysics modeling. It has the genuine look and feel of a Macintosh application. Thanks to the power and fl exibility of the FEMLAB 3 solvers, Macintosh users now can perform all of their scientifi c modeling on Mac OS X. Says Prof. Bruce Finlayson at the University of Washington in Seattle of his early FEMLAB-for- Macintosh results, “I ran a 3D linear problem with 267,293 degrees of freedom—the convection diffusion equation with a known velocity. I was astounded when it ran in 87 seconds”.

Lars LangemyrVP OF DEVELOPMENTCOMSOL

FEMLAB enables in-depth learning despite big class sizeDr. Alison Flatau of the Aerospace Engineering Department at the University of Maryland taught numerical modeling to a 68-student junior level aerospace structures class last quarter. One immediately expects that the large class size would minimize participation and learning opportunities. On the contrary. Dr. Flatau overcomes the size issues with well-defi ned problems, a little creative footing, and the old one-two-three: (1) experimentation, (2) analytic solutions, and (3) computer models. For example, her students create simple stress-concentration models, by notching and stressing transparency paper. These inexpensive experimental models are matched to complicated analytic solutions that the students derive, at length. The virtues of FEMLAB appear when students are able to quickly predict their experimental and analytic results with a FEMLAB simulation and then go on simulate far more complicated problems. Says Flatau of the experience: “Because FEMLAB is so straightforward to use, the students can attempt, interpret, and learn from their own multiple-iteration stress-concentration tests.”

FEMLAB modeling a focus in next release of widely read chemical engineering text

H. Scott Fogler, a long time FEMLAB enthusiast, is including many FEMLAB examples in the upcoming release of “Elements of Chemical Reaction Engineering”. Used by approximately 75% of the chemical engineering programs in the United States, this book has been the dominant chemical engineering text worldwide for many years. Dr. Fogler is the Vennema Professor of Chemical Engineering at the University of Michigan and the recipient of numerous research and teaching awards.

For a taste of what to expect next January, visit the CRE home page at www.engin.umich.edu/~cre/web_mod/radialeffects

Zurich is into modelingStarting this fall (2004) FEMLAB sales in Switzerland will be handled out of Zürich. Dr. Sven Friedel has been appointed the job of managing director. With a background in modeling geophysics, Dr. Friedel is well prepared to serve the Swiss FEMLAB users.

FEMLAB 3.0a SYSTEM REQUIREMENTS FOR MAC OSX

FEMLAB 3.0a runs on Mac OS X v10.3 Panther. The minimum system confi guration is a G4 with Java 3D and Java Advanced Imaging and at least 256M bytes of RAM (512M bytes recommended).

:


A technology leader in the heavy-duty filtration industry, Fleetguard (a wholly owned subsidiary of Cummins En-gines) uses FEMLAB to analyze separators that remove particulates from airflow streams. In operation, an electro-static separator first builds up a corona field around a high-voltage electrode. Particles passing through the field pick up a positive charge and then are attracted to a grounding element such as a plate. A higher voltage creates a more powerful corona field and thus a more efficient filter—but when the field strength exceeds a certain level, sparking within the device can arise. Lost efficiency is only one neg-ative consequence of sparking, which can also cause pre-mature failure of the power supply. Clearly, the designers want to find a field strength that has the highest efficiency that will not provoke sparks. Beyond voltage, two other key variables that affect electrostatic separator performance are electrode size and shape. Further, the current in the corona and sparking depend on the field in a highly nonlinear way and are sen-sitive to small local variations in field strength. While it is possible to fabricate and test various configurations in the lab, engineers at Fleetguard knew it is far more efficient to examine design options in software. Finding the right software was a challenge in itself. “We’re part of a large corporation and thus have access to many modeling packages,” notes research engineer Ismail Bagci, “but our primary concern was examining the elec-tric field, and none of those packages were able to handle the job to our liking. We looked around and decided that FEMLAB offered capabilities we needed at an attractive price.” “Even though we bought the package primarily for its ability to analyze electric fields,” he adds, “we purchased all the optional modules. FEMLAB’s ability to combine sev-eral multiphysics aspects easily has broadened its use into

>

In this symmetric section of a filter canister, the red geometry shows the electrode, whereas the green isosurfaces show the electric field. The large isosurfaces at the top and the bottom, where the field protrudes out from the elec-trode, reveal areas with greater probabilities of high-voltage sparks.

the exploration of other filtration problems we studied pri-marily through experimentation. We’ve barely tapped the package’s enormous potential, and we’re still learning what it can do for us.” Apart from looking just at the corona field, the team can simultaneously study flow. Air flow through the de-vice fluctuates between laminar and turbulent as the en-gine runs in different conditions, but the designers need to know what flow looks like at all times. The group modeled turbulence simultaneously coupled with electrostatic prop-erties and particle tracking. This study is important because if a charged particle touches a boundary wall or another particle, it tends to be held in place. By looking at the com-bined physics (flow characteristics along streamlines, parti-cle size, electric forces, mass and density), a more accurate simulation results. Multiphysics capabilities also prove quite useful when exploring particle tracking through porous media. The de-sign goal is a permeable basis in the filter that collects par-ticles effectively under all conditions. “This isn’t the kind of capability you find in a standard package,” notes research engineer Kevin South, “so we asked one supplier of modeling software if they’d help us cre-ate a particle-tracking routine. They said it was possible but would be a ‘major undertaking.’ We then approached comsol, and they wrote our routine in a week.” It consists of Mat-lab code, which provides a tightly coupled computational engine behind FEMLAB for such applications. The group also harnessed FEMLAB’s integration with Matlab in other ways. They wrote a geometry-generat-ing program that quickly creates simulated fiber environ-ments based on the supplied physical parameters for fiber

We looked around and decided that FEMLAB offered capabilities we needed at an attractive price.

In this cross section of the fiber media, the blue lines represent particles along a streamline whereas aqua-colored points represent captured particle or particles. FEMLAB can model the particle tracking of an entire particle perimeter rather than just its center of mass.

A cross section of the fiber media shows each fiber as a white circle so the researchers can run a velocity profile for various types of fluid passing through the filter. One way they get the fiber distribution is to take a photo of the media, create a DXF file and import it into FEMLAB. To try other configurations, they run a Matlab subroutine that creates a random arrangement of fibers of various sizes and positions, and then FEMLAB examines the flow paths and velocities. An animation goes a step further to show particles being captured in the media.

We’ve barely tapped the package’s enormous potential...

>>

Research engineer Ismail Bagci modeling the flow through a cross section of a fiber medium.

CONTINUES ON NEXT PAGE

With air pollution on the rise and the EPA (Environmental Protection Agency) heading it off with strict regulations, auto manufacturers look to multiphysics modeling to take a serious bite out of engine emissions. So many of the items that we take for granted (such as air, fuel, and water) stand to benefit from filtration design advances. Fleetguard brought about a series of major advances when they began optimizing the performance of an electrostatic particle separator through FEMLAB simulations.

BY PAUL SCHREIER

filtration systemsnext-generation

Multiphysics software speeds analysis of


media. Importing DXF files from microscopic photographs allowed for more complex media-structure modeling. Then, with comsol’s sub-routine, the team monitored injected batches of mono-disperse particles for particle surfaces touching any fiber surface in the model domain (walls) as well as contact with other “tagged or halted” particles. This is a unique capability not possible with other specialized codes that can only track a particle’s center of mass and not the entire perimeter. “Our ultimate objective,” notes principal engineer Peter Herman, “is modeling the depth loading characteristics of our gradient StrataPoreTM filter media to maximize its capac-ity and efficiency for liquid-filter applications. Of special interest for particle capture in fibrous liquid filters is “interception” mode, where a particle doesn’t inertially deviate from flow streamline but is captured anyway due to the edge of a particle contacting a fiber. Thus FEM-LAB’s ability to track particle perimeter versus simply the center of mass is a prerequisite.” With FEMLAB’s Structural Mechanics mod-ule, the researchers have modeled 2D and 3D pressure vessels and cross-sectional housings to develop an understanding of the unit’s burst and fatigue properties. The only stumbling block the engineers encountered was importing 3D models they created in ProEngineer, whose drawing capabilities they prefer for sophisti-cated configurations. After drawing a filter with ProEngineer they must create an IGES file, read that file into SDRC (now part of the PLM family at EDS), have that package create an IGES file, and then read it into FEMLAB. This method was necessary with FEMLAB ver 2.3, but with the latest release, ver 3.0, COMSOL reports that such importing problems have disappeared. The designers were also impressed with FEMLAB’s speed. The model for a typical elec-trostatic particle separator has close to 40,000 elements, and a standard electrostatic model solves in less than 10 minutes; a multiphysics model takes from 20 to 30 minutes. With their first few designs, they compared the results from FEMLAB from those with another mod-eling package that took three times as long to run, and the results were identical. They also corresponded very closely to laboratory find-ings. With this confidence, Fleetguard started examining a variety of electrode designs, evalu-ating far more than they could with any other package and far, far more than they could if they had to do the work experimentally.

The best way to describe improvements added by the software is to work through an engineering problem, such as a sensor redesign. Our company produces an asphalt sensor that meas-ures to a depth of 4 in. We wanted to apply this sensor to measure soil to a 12-in. depth but needed to limit its diameter. The primary design parameters were the shape and configura-tion of the sensing plates and associated ground planes. As there is no closed form solution for the electric field for this configuration, we resorted to simulation with femlab. The software lets users model in 1d, 2d, and 3d, but because the soil-sensor concept is symmetric, we used a 2d axisym-metric mode for the electrostatics applications. Two-dimen-sion models minimize computation time and memory require-ments, while still providing excellent insight into resultant field patterns. For example, sensor components and solids are represented by simple rectangular regions. After model build-ing, the software translates the solid objects into subdomains and boundaries to which users assign material properties and boundary conditions. Because the soil sensor consists of re-gions with different electromagnetic properties, such as con-ductivity and permittivity, they are placed into separate sub-domains. To assist postprocessing, users may further subdivide homogeneous subdomains at important locations. In the sen-sor model, soil is subdivided into horizontal slices to assess values of interest at specified depths. Boundary conditions are assigned by specifying external voltage and currents. Geometry boundaries must exist where boundary conditions will be ap-plied. Boundary condition values are specified in a dialog box or defined externally in the Constants dialog box (in Options menu) and symbolically specified in Boundary Settings. The software assists by assigning sensible defaults for each bound-ary, such as field continuity for internal dielectric boundaries between domains. To build an adaptive mesh, users need only pick Initialize Mesh. If the automatic process does not produce an acceptable mesh, several levels of semiautomatic and manual controls are available to govern all aspects of mesh generation. The solve step finds a continuous solution for the entire model. On a 2 GHz P4 processor with 1 Gbyte ram and run-ning xp, the sensor model took 8 seconds to solve. The time to solution depends on the physics, model, and mesh complexity. The software then presents a default solution plot. In this case, it was a surface plot of potential across the view plane. The software also superimposes an arrow plot of the electric-field vector. Values that would determine depth include the

capacitance in each measurement subdomain and contour lines of the resultant displacement vector. To measure depth, the software calculates the capacitance in each subdomain meas-ured by the sensor. A general formula for capacitance is:

where V = potential across the domain and We = energy den-sity. The integral is computed using a postprocessing integra-tion function over the subdomain. We arbitrarily define the measurement depth as the depth at which the integrated capac-itance is equal to 99.5% of its final value. But the Subdomain Integration function only calculates total energy, so its value was exported into Matlab. At the Matlab command line, capacitance is calculated using the equation above. One idea for increasing the measurement depth without increasing sensor diameter is to remove the ground plane on the current sensor for asphalt. We thought field lines from the transmitter that are divert-ed to the ground plane would then pass into the soil. But the femlab solution for the modified sensor mod-el illustrated the opposite: the ground plane allowed deeper penetration, the opposite of what was expected. Results showed field lines flowing from transmitter to ground penetrating deeper than those flowing from transmit-ter to receiver. This unexpected result steered the design in a different direction. Relocating and spacing the ground plane increased the penetration depth. The end result was a 100% in-crease in measurement depth with only a 10% increase in sen-sor diameter. Lab tests of a prototype agreed with simulation results. In the design process, a problem developed with a bound-ary condition on an internal electrode that let the software technical support team demonstrate their quick response. The electrode has a floating potential that depended upon exter-nal circuits and properties of the material being measured. So this potential could not be specified prior to solving. femlab’s documentation and sample library did not provide a method to apply floating potentials. However, an e-mail describing the problem and a call to the regional technical representative produced a timely solution and explanation. An entry regard-ing the problem and solution was later placed on the comsol website so others can benefit from the experience. FEMLAB is an intuitive, easy-to-use tool that provides in-sight to the detailed workings of complex devices. We estimate the software paid for itself on the first project.

USER REVIEWRectangular slices of soil were simulated using 1-in.-thick layers. But simulations revealed an irregular shape to the response field. So the soil geometry was modified using a Bezier curve tool to produce subdo-mains that precisely reflected the measured volume. This shortened run times.A close up on FEMLAB for

soil-sensor design

CONTINUED FROM PREVIOUS PAGE.

Ronald W. Gamache is the director of Research and Development with TransTech Systems, Inc. (www.transtechsys.com). The company offers a wide range of products for asphalt paving and has achieved a worldwide reputation for innovation across various levels of the roadbuilding industry. By using FEMLAB they acquired new insights into their sensor technology. Here Mr. Gamache gives his team’s review of FEMLAB.

BY RONALD W. GAMACHE

Ron Gamache of Trans Tech Systems, Inc. analyzing soil sensor data.

Visualization plots illustrate the per-formance differen-ces between design options. Moving the ground plane (below) increased the sensing depth.

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FEMLAB simulations ramp up

In fiber optics systems, information from an electronic source is converted into light signals. The light is guided into a glass fiber and travels down its optical core. The light remains within the fiber because the refractive index of materials surrounding the optical core of the fiber is far lower than that of the optical core itself. When the light signal arrives at its destination, it is converted into the elec-tronic form for further processing. Optical processors, such as those that Enablence de-signs, manipulate the light at critical points along its path. At the source, a processor may multiplex light signals to a denser form. At the destination, optical processors can de-multiplex the dense signal into fundamental wave lengths, which eases the conversion back to electronic form. And so on.

VIRTUAL TEST ENVIRONMENT

Dr. Serge Bidnyk uses FEMLAB in an iterative design strat-egy to develop optical processors for Enablence. To avoid unnecessary constraints on the design, he chooses materi-als and manufacturing methods that are as non-restrictive as possible, including innovative deposition techniques, advanced oxide etching, and metallization. What the FEMLAB simulations offer the design process is a “virtual testing” ground—he makes predictions for (and learns from) unusual designs, extreme conditions, limiting behaviors, impacts from coupled processes, to name a few (e.g. Fig.1). Required for the physics-based predictions is the capac-ity to handle: arbitrary geometries; individual and coupled processes (e.g., Maxwell’s equations, heat transfer, stress/strain, chemistry); user-defined governing equations; vec-tor equations; inhomogeneous and anisotropic material properties; complex numbers in material properties; freely prescribed boundary and initial conditions; flexible post-processing, and full access to the solvers via a scripting program. Dr. Bidnyk says he chose FEMLAB because of its unique ability to meet all these analyses requirements. When questioned about the user flexibility aspects, he ex-plains, “No other package would let me get anywhere near as close to the simulation engine as would FEMLAB”.

AN ITERATIVE DESIGN CASE

Consider the DWDM (dense wavelength-division mul-tiplexing) optical processor designed by Dr. Bidnyk us-ing FEMLAB simulations. The DWDM typically consists of a substrate and a series of waveguide cores with either a surficial cladding or some filling material to encase the core. How a given frequency signal travels through the core, or the mode number, is determined by the way the light bounces off the channel walls. There can be, for in-stance, 20 or 30 modes for just one color of light, each with its own intensity profile and characteristic speed. A 10 mm x 30 mm device will handle 40 optical waveguide cores. With each channel carrying 40 GHz of information

design of processors for

Optical fibers transmit far more information with less interference and at much higher speed than conventional copper wiring. In just one decade, gains made with fiber optics have indelibly raised our expectations of world communications. But before this promising technology can displace legacy copper networks altogether, inexpensive means to produce large quantities of tiny optical processors must be found. Enablence, Inc. from Ottawa, Canada, is using multiphysics simulation with FEMLAB in an extremely successful design program for the optical processors.

Fig. 1. FEMLAB helps determine the modes of a given frequency of light within the optical core. With this analysis, designers can optimize the geometry to eliminate the effects of birefring-ence as well as find the modes with the best propagation properties. This image shows how periodic bounary conditions can approximate real-world effects.

fiber optics communication

bandwidth, a total bandwidth of 1.6 terabits per optical link is obtained—this level of information transfer eclipses anything possible with electronic systems. In a given design loop, Dr. Bidnyk would use FEMLAB to address the same well-defined question for incremental-ly different DWDM configurations. Typical questions are: What is the intensity distribution in the waveguide core? What is the passband performance for this waveguide? Which Eigenmodes are sustainable in the waveguide? or What is their speed of propagation? Once the question is decided, the simulations are conducted in a rapid fire batch mode. To minimize computational time and duplication of effort, he finds the simplest geometry that represents the system without losing valuable detail. The results of the batch simulations can be used to cull geometries that do not work and identify the interesting work-able ones that should receive further attention and analysis. For just one DWDM configuration, a simulation pro-cedure is established, typically with the FEMLAB graphical user interface (GUI). The appropriate governing equation is chosen, for instance, Maxwell’s vector wave equations

The biggest problem in optical processing is birefrin-gence, which plagues the ability to process light.

Fig. 2. A semiconductor wafer can contain thousands of photonic processors. In this photo you can see a dozen separate devices, each a rectangle of less than 0.2 square centimeters. Each device is capable of proces-sing far larger amounts of information compared to anything possible with elec-tronic systems.

>>

Dr. Serge Bidnyk of Enablence uses FEMLAB to optimize photonic processor design. For more informa-tion contact Dr. Bidnyk at [email protected]


BY PAUL SCHREIER & LE IGH SOUTTER


for a complex permittivity tensor. Then the geometry is defined, material property values are entered, and bound-ary conditions are set. The material properties may involve complex numbers. The boundaries typically are some combination of absorbing, periodic, metallic and magnetic boundary conditions. Once the problem is set up, the ap-propriate solver is chosen. Where possible, Dr. Bidnyk uses the adaptive meshing algorithm, which instructs FEM-LAB to automatically zoom in on areas where the solution changes rapidly. During postprocessing he may generate graphics and evaluate certain quantitative results. The set up for Eigenvalue analysis of the DWDM is straightforward (Fig. 3). Since the device has 40 waveguide cores lying side by side and sandwiched be-tween substrate and fill, the geometry is symmetric—the same slice is repeated 40 times. Only a representative zone of the DWDM need be modeled. Periodic boundaries are placed where the solution would repeat. With roughly 4000 elements to the cross-section, finding the Eigenvalue solution requires approximately two minutes. The results

between thermal, mechanical, electromagnetic, and/or chemical impacts. Consider birefringence, for example. Birefringence is an optical property whereby the refrac-tive index of a material differs with the polarization of the light. Inherent birefringence arises during the manufactur-ing process because materials are stressed as the hot wafer cools down. Form birefringence occurs when the refrac-tive index varies with geometry. Comments Dr. Bidnyk, “The biggest problem in optical processing is birefrin-gence, which plagues the ability to process light.” Because the polarization of light is unknown during transmission in the cable, it is critical for a device to operate identically at any polarization. To examine birefringence with a numerical model re-quires vector analysis. Only a very few software packages offer this capability, and FEMLAB is among them. Dr. Bidnyk uses FEMLAB to account for inherent and form birefringence in separate steps. For analyzing inherent birefringence, he adds a simulation of mechanical stresses and assigns inhomogeneous and anisotropic optical prop-erties to the waveguide. Now the model can handle differ-ent growth and annealing temperatures and yield precise values for the stress-induced birefringence. For form bi-refringence, he uses the inherent birefringence analysis (as above) and then finds a core geometry with a form bire-fringence that compensates for the inherent birefringence, resulting in a device that is essentially polarization-insensi-tive. FEMLAB’s unusual capacity to do both vector analysis and accept refractive indices built with complex numbers (as above) also allows Dr. Bidnyk to analyze other difficult-to-address issues. Consider what doping types and levels will achieve desired amplification and attenuation rates. “Some packages just won’t accept complex numbers,” ex-plains Bidnyk, “but FEMLAB does, and my algorithm can thereby calculate attenuation for any core geometry.” This capability is very helpful for considering advanced design options. Device engineers, for example, could dope core material during manufacturing to alter its amplification or attenuation properties. With the complex part of the re-fractive index, he can determine to what degree the doping will change how the core attenuates or amplifies the light passing through it.

DENSE YIELD, LOWERED COST

Clever design strategies, such as Dr. Bidnyk’s, are making it possible for Enablence to produce high-performance chips at dramatically lower cost. Careful miniaturization is increasing the density of photonic devices that will fit on a single wafer: common photonic technologies produce 5 to 30 chips on a wafer, but Enablence packs as many as 3000 chips on each one (Fig. 2). These small chip sizes bring high manufacturing yields as they limit the impact of wafer defects and nonuniformities. Moreover, the high density lowers packaging costs, which are a significant factor in the cost of photonic and optoelectronic products.

Fig 3—A finite-element mesh of a typical photonic device shows the major divi-sions. The waveguide cores in the center are surrounded by a cladding or filling material that has a far higher index of refraction, thus containing lightwaves within the optical core channels. Each such channel can accommodate optical transmission rates as high as 40 GHz.

(Fig. 1) reveal that the periodic boundaries are effective at simulating the desired symmetry condition. What if you have hundreds of variations on one DWDM design? Learning how to perform a little automation with a Matlab routine suddenly is extremely important. First, open the DWDM model (above) in the FEMLAB-with-Mat-lab GUI, and save it as an M-file. Now to run the FEMLAB model from the Matlab command line, simply enter the filename. All that remains is to modify the M-file with a Matlab script so that it repeats the FEMLAB commands for each geometry. With an eigenvalue solution in two min-utes and a Matlab automation routine, Bidnyk can analyze hundreds of geometries per day. “I couldn’t really consider using any other tools,” says Bidnyk. “The fact that FEM-LAB can be run from the Matlab command line results in enormous time savings,” he adds.

ADVANCED ANALYSES

Results from batch mode simulations can be used to iden-tify which designs merit in-depth analysis, like coupling

Everyone tolerates the chlorine taste of tap water because we all know it symbolizes an important path against pathogens. But when the chlorine tanks in water treatment plants malfunction, cancer-causing disinfection byproducts may be produced. Dr. Eric Vogler of Boyle Engineering used FEMLAB simulations to design a baffling system that prevents tank short-circuiting and still maximizes volume mixing with chlorine.

Chlorine pulse moving through baffling system water treatment tank. Simulation couples the k-ε Turbulence and Transient Convection-Diffusion application modes from FEMLAB’s Chemical Engineering Module.

Go ahead, drink the water!

Fig. 3. A finite-element mesh of a typical photonic device shows the major divisions. The waveguide cores in the center are surrounded by a cladding or filling material that has a substantially lower index ofrefraction, thus containing lightwaves within the opti-cal core channels. Each such channel can accommodate optical transmission rates as high as 40 GHz.


Example of 3D modeling capabilities from SolidWorks.

COMSOL adds interaction with leading 3D CAD productsNew capabilities for integrating CAD tools with FEMLAB are under way! Starting this summer the COMSOL offices in Sweden and Finland will also offer SolidWorks along with their product line. We at COMSOL are very excited—this is one giant step toward synthesizing industrial strength CAD and FEMLAB physics modeling capabilities.

Chalmers purchases 3-year site license Chalmers University, Sweden, recently made it official—they are committing to FEMLAB on a very large scale. This is good news to the 12,000 students, teachers and researchers, who get unlimited access to FEMLAB, the FEMLAB modules, and all updates and new releases from COMSOL during the 3-year site license agreement.

Stanford students across the campus focus on the science, not the code Dr. Tapan Mukerji, Dr. Youngseuk Keehm, and Dr. Amos Nur all teach FEMLAB modeling in their physics-based numerical methods courses at Stanford University. An enthusiastic advocate for the new university-wide site license, Dr. Mukerji exclaims, “FEMLAB lets researchers and students apply state-of-the-art finite element tools for practical problem solving, which allows them to focus on the science rather than on developing and debugging code.” Take a look at some of their lessons plans: water.stanford.edu/GP200

Substrate

Waveguide cores

Filling material

Metal electrodes

Learn FEMLAB from a proJohn Dunec, head of Venture Product (Palo Alto, California), teaches a periodic series of courses on how to use FEMLAB to solve multiphysics problems. Included in each series are day-long introductory and intermediate sessions, with a third day focusing on an advanced topic, such as MEMS or microfluidics. John is a Stanford University PhD with a long history of numerical modeling in industry and consulting for a wide range of processes.

What about amoeba modeling?

Dr. Peter Thomas of the Salk Institute (San Diego, California) attended one of John’s recent classes. Dr. Thomas’ focus is biological computation—addressing some biochemical reaction for a living cell with a numerical model. Of his experience in John’s class, he writes, “John Dunec did a terrific job as instructor. He was informative, knowledgeable, entertaining, and most importantly, flexible.” Flexible indeed! One day in class, Dr. Thomas asked John how to simulate the creation of a pseudopod protruding from the surface of an amoeba. While by no means a typical classroom (or consulting) request, John brought his vast professional experience (and FEMLAB’s ease of use) to bear on the amoeba problem. And that very same afternoon Dr. Thomas walked away with a good start on the model that he needed. Now that was a good use of class time.For more information about John’s classes see:www.ventureproduct.com.

FEMLAB classes in Palo Alto. In the foreground are Dr. Don Gervasio (Arizona State University) and Dr. Tapan Mukerji (Stanford University) on the left and right, respectively.

Periodic boundaryconditions


[email protected]

I am trying to calculate the capacitance and inductance of a component, and I am finding a strong dependence on the mesh resolution. Is there anything that can be done to improve the accuracy of the result without requiring the use of an extremely fine mesh?

Scott Corzine AGILENT TECHNOLOGIES

PALO ALTO, C A, USA

Yes. In your case, you need to integrate potential gradients on boundaries to get the total surface charge:

Where n is the normal vector of the surface and D is the electrical displacement field

Using the potential difference between the electrodes, ΔV, the capacitance is given by

The problem with evaluating gradients on boundaries is that the accuracy can suffer and may depend on the mesh and the shape of the boundary. FEMLAB provides an elegant solution to this problem by using weak boundary constraints. In FEMLAB 3.0, weak boundary constraints can facilitate very accurate integration of the normal flux density across boundaries with Dirichlet type conditions (fixed potential, temperature, displacement etc.). Use the menu option Physics >Model Properties >Weak Constraints: Non-ideal.

I have four application modes, one for pressure, two for mass fractions and one for temperature. Can I use different element orders for the various solution components and even use different orders for each subdomain? Or do I need to have the same element order everywhere? (Quadratic, cubic, etc.).

Bengt Fallenius ROYAL INST ITUTE OF TECHNOLOGY,

STOCKHOLM, SWEDEN

In most cases you can have different element orders or types for different variables. There are a few exceptions. For example, a variable that is used to implement a constraint on another variable must have the same order as the constrained variable. This is the case in the Incompressible Navier-Stokes, where the pressure needs to be of one order lower than the velocities. This mixed element setting is defaulted in the FEMLAB Navier-Stokes application mode. It is also possible to have different element orders on the same logical quantity in different subdomains. But then you need to use two variables and a constraint on the subdomain interface to connect them. This is rather complicated and not recommended.

I want to combine different application modes in the Structural Mechanics module—shells and 3D solids in the same model. How do I deactivate the shell in the geometry portions where I don’t want to use it?

Massimiliano Moruzzi IMTA INC .

ROCKFORD, IL , USA

Then you can integrate the new variable name, for example lm1, to get a very high accuracy surface charge, flux, stress etc. The name of the new variable can be seen on the Weak Constraint tab in the Boundary Settings dialog box.

I wonder if I can specify varying material properties. For example, I have a material in which the electrical conductivity varies with the coordinates. What about (strongly) anisotropic materials?

Willy Peelen TNO BOUW

DELFT , NETHER LANDS

The spatial coordinates are always available as the x, y, z variables. You can type arbitrary mathematical expressions in most edit fields. For example, 0.45 + .003*x is a valid specification for a linearly increasing conductivity. For time varying quantities you can use the variable t for time. Anisotropic and orthotropic materials can be directly entered in matrix/tensor format in the dialog boxes for the material properties. You can also use step functions or smoothed step functions for sudden switches in material property values.

The Support Knowledge Base at www.comsol.com/support/knowledgebase is your first stop for support. Search the Knowledge Base if you are looking for solutions and explanations to issues concerning installation, run-time diagnoses, or any question on modeling using FEMLAB. Following are some Support Knowledge Base cases.

The COMSOL support team will ensure that you get the most out of

FEMLAB. Contact us to get instant help with any questions concerning

your FEMLAB use. We’ll address issues across the board, such as modeling

practice, mathematics considerations, applied engineering and physics,

installation issues, and product and licensing information. The support team

offers global service and consists of approximately 20 specialists, most of

whom hold doctorates in various engineering and physics fields. Many of the

engineers have a long background in industry.

You can reach the support team by sending an e-mail to

[email protected]. In almost all cases we respond within 24 hours.

You also can get assistance on the telephone by calling your local FEMLAB

representative.

What is the FEMLAB Model Library?

I want to extract my FEMLAB data

for external postprocessing with

other software.

Yes, you can define your own variable transformation in FEMLAB. If you want to express, for example, material data or dipole fields in terms of r, phi, and theta, just draw your geometry in cartesian coordinates and then define three expressions in the Scalar Expressions dialog box under the Options menu.Define the followingName:Expression pairsr: sqrt(x^2+y^2+z^2)phi: atan2(y,x)theta: acos(z/r)

The mathematical functions sqrt, atan2, and acos are built-in functions in FEMLAB. Once you have defined the expressions, you can express whatever you want in terms of r, phi and theta. If you have an axially symmetric model, you can use FEMLAB’s built-in axisymmetric application modes in the r-z space.

See also www.comsol.com/support/knowledgebase/939.php

From the File menu, select Export and then Postprocessing Data. You will get a dialog box with a multitude of options to tailor your data export.www.comsol.com/support/knowledgebase/829.php

The purpose of the Model Library is to demonstrate the full power of FEMLAB and to help users come up to speed quickly with its operation. The Model Library contains examples of FEMLAB models which cover many classic problems and equations from various fields of science and engineering. These examples demonstrate the package’s versatility

and reveal the wide field of applications to which users can successfully apply FEMLAB. These familiar examples also present an educational basis upon which users can learn about the software and get a glimpse of the physics underlying these classic cases.

See also www.comsol.com/support/knowledgebase/791.php

ABOUT COMSOL SUPPORT

Fig. 1. Clear the “Active in this domain” checkbox to deactivate an application or set of equations on a certain part of the geometry.

> Can FEMLAB handle polar coordinates?

>

>

Would you like to hear about some of the

many questions we have received from

FEMLAB users? Our goal is to offer tips

and tricks that will make your modeling even

better. Take advantage of our experience

and send us a question or two. You can reach

us at [email protected].

Have fun modeling!

B Y N I K L A S R O M

C O M S O L S U P P O R T T E A M

From the Multiphysics menu select Shell. Then select Boundary Settings from the Physics menu. Select the boundary you want to deactivate, clear the checkbox Active in this domain. (Fig. 1)

In one of my transport models I have an equation of the principal form

Where is the variable I want to solve for, B is a constant and is a rather involved analytical expression in , that is . I am not sure how I can enter the gradient without having to perform the tedious differentiation with respect to .

Frank Zalar MATER IALS SC IENCE & ENGINEER ING

OHIO STATE UNIVER S ITY, USA

FEMLAB can do automatic symbolic differentiation with the built-in operator diff. Assuming you are using the 2D PDE General form application mode in FEMLAB to solve for Phi, your task will be to enter the x- and y-components of the flux vector.

The steps will be 1) Define an expression in the

expression list that defines the function . Let’s call it mu. Also define the constant B.

2) In the edit field for the flux vector, type –B*diff(mu,x) and –B*diff(mu,y), respectively. (Fig. 2)

Fig. 2. Built-in auto-matic symbolic dif-ferentiation enables powerful equation-based modeling.


A DEVICE THAT AIMS HPMS AT A TARGET

SARA develops cutting-edge, multidisciplinary technologies in areas with high scien-tifi c and/or market potential and transforms these new technologies into successful products and services for clients in business, industry, and government. The folks at SARA already know a device that aims HPMs at a target is an important contribu-tion—a powerful but non-lethal weapon that blows out the defense, vehicle, and communications systems of a national enemies and fl eeing criminals. The method is non-lethal because HPMs emit very low levels of radiation, well within the range assumed safe to humans by health experts. Since the co-axial cables that convention-ally transmit microwaves cannot be used with HPMs, SARA scientists are using FEMLAB to develop new pyramidal horn waveguides that will solve their problem.

Simulations key to

Scientifi c Applications and Research Associates (SARA), Inc. of Cyprus California is using femlab in a funded project to develop an antenna that supports directed transmissions of high-power microwaves (hpms). With power levels up to 100 megawatts, the hpm signals are so potent—enough to power a small town—they actually degrade electronic circuits in their path. Even co-axial cables cannot withstand the large volumes of power.

The complete HPM antenna consists of two re-fl ecting surfaces as well as the feed horn with its resonant window. This system emits microwave pulses that can disrupt electronics and disable a vehicle or weapon.

>>

nonmmicrowave weapon

non-lethal

Senior Scientist, Dr. Robert Koslover (left), of SARA Inc. and Mr. Benson King of the Army Research Lab standing in front of the microwave pulse antenna.


BY PAUL SCHREIER & LE IGH SOUTTER


meshing and accuracy. With the fi nite-element method that FEMLAB uses, he can vary the size of the mesh, insert-ing tiny elements in critical zones, near the window for ex-ample, and switch to a coarser mesh where properties and conditions are relatively uniform, beyond the horn. With the FDTD (fi nite-difference time domain) codes he also considered for this job, getting high accuracy necessitated extending the fi ne mesh he used near the window through-out the entire model. This would have amounted to pro-hibitively long run times and enormous computational cost. Given that his FEMLAB model consists of 89,000 elements or 115,000 degrees of freedom (Fig 1), it runs in reasonable time on his personal computer—a 1.7-GHz P4 machine with 1 Gbyte of RAM. As to accuracy, the VSWR estimates from FEMLAB simulation are a near perfect match to the experimental data (Fig 3). The VSWR estimates from the FDTD code, however, are relatively poor. With the good fi t for the one geometry, Koslover gained confi dence that he could use FEMLAB for continued modeling and yield reliable results for other designs. In fact, after a number of simulations he arrived at a design of particular promise, one with a low VSWR, a ratio of 1.2:1, which he considers to be especially good. The HPM antenna is adding to what already is an im-pressive list of non-lethal methods that SARA is developing to disable unwanted threats. Consider the possibility of a sonic fi re hose, multisensory grenades, or a vortex launch-er. For more information on SARA and its work with non-lethal weapons and HPMs, visit www.sara.com.

Fig 2. The feed horn with its resonant window.

Fig 3. A comparison of the measured and mo-deled values for VSWR (voltage standing wave ratio) on the HPM an-tenna shows a very good fi t, so the researchers are confi dent they can model other window geometries successfully.

Fig 1. In this FEMLAB model of the waveguide, horn and window, note the standing waves that arise in the long feed waveguide when the horn and window are driven at an off-resonant frequency.

As to accuracy, the VSWR estimates from FEMLAB simulation are a near perfect match to the experimental data

(VSWR). The VSWR is the ratio of the maximum voltage to minimum voltage. A window giving VSWR close to 1:1 is optimal because it indicates low energy loss; i.e., a mini-mum of energy refl ects off the window, returns back into the horn, and burns up as heat rather than proceeding to the target. A good design also minimizes the potential for air breakdown (and arc formation) just beyond the win-dow.

DESIGN TESTING WITH FEMLAB

Dr. Koslover designed and tested a range of window ge-ometries and dielectric materials for the pyramidal-horn antenna using a computer simulation approach with FEMLAB. An advantage to this approach is that working with simulations in addition to physical testing not only minimizes the time, material and laboratory costs of pro-totyping, but it also adds new insights about the physical processes. Another distinct advantage to his method is his design criteria—calculating the VSWR offers an objective means to rank design effi ciency. In a typical problem set up (Fig 1), Dr. Koslover simu-lates HPM propagation throughout the waveguide for each window geometry. Absorbing, PMC (perfect magnetic conductor), and PEC (perfect electric conductor) bound-ary conditions are applied as appropriate. The VSWR is calculated as a postprocessing step for each frequency sim-ulated (Fig. 3). During calibration, the VSWR results are compared with experimental data. Otherwise, the VSWR is used to evaluate new window geometries. Why he chose FEMLAB to zero in on the best pyrami-dal horn design was easy for Dr. Koslover to explain:

CRITERIA FOR A GOOD DESIGN

FEMLAB simulations (Fig. 1) enabled Dr. Robert Ko-slover, a senior scientist at SARA, to design and fi ne tune the feed horn for the HPM antenna. A feed horn is a horn-shaped medium for propagating electromagnetic waves, a “waveguide” that conveys electromagnetic signals between a transceiver and refl ector. At a glance, the pyramidal feed horn from the HPM antenna (Fig 2) would be mistaken for a commercial L-band (1.1-1.7 GHz) microwave feed horn except for the thick dielectric window on the face of it. The dielectric window came about because the strong elec-tric fi elds associated with the HPMs actually break down air molecules and produce an electric arc. Having the feed horn enclosed by a window allows the designers either to remove air from within the horn or fi ll it with a gas that slows down electrons and eliminates the arc. Another function of the window is to act as a conduit for the microwave energy; after all, the window is not present in other feed horn designs. It follows that the energy should pass through the window with minimal at-tenuation and dis- tortion. Dr. Koslover explains that the best way to determine which

window geometries work best for the HPM antenna—

thickness, shape and curva-ture—is by screening the

designs for those with an output radiation

pattern that yields a small voltage stand-ing wave ratio

TRAINING COURSES

Do you want a head start in using FEMLAB? What about a few time-saving tips to speed up your modeling? If so, then Introduction to FEMLAB is the one-day training course for you. This hands-on workshop is suitable for anyone interested in using FEMLAB for mathematical modeling of physics phenomena such as heat transfer, transport phenomena, fl uid dynamics, electromagnetics, photonics, structural mechanics and acoustics.

Why don’t you join us for one of our one-day sessions? They are being offered all over the globe. To get more information, register for a course, or browse event locations, please visit: www.comsol.com/training.

WORLDWIDE SEMINARS

The spring 2004 tour attracted over 5,600 attendees from all over the world. With new and exciting product releases coming soon, we are gearing up to handle an even larger crowd during our next 2004 Fall Seminar Tour. Sign up now for a seminar close to you.

Even if you are not a current FEMLAB user, our seminars offer a learning opportunity you don’t want to miss. Please join us at any of our free seminars and software demonstrations to see models being built from scratch, and discover how FEMLAB can help you in your work. To get more information, register for a seminar, or browse seminar locations, please visit: www.comsol.com/seminars.

INTERNATIONAL CONFERENCESWe will show FEMLAB at these upcoming conferences:

2004 ICMENS

Banff, AB, Canada August 25-27, 2004

DECHEMA/GVC

Jahrestagung 2004, Karlsruhe, GermanyOctober 12-14, 2004

2004 Fuel Cell Seminar Conference

San Antonio, TX, USANovember 1-4, 2004

FEMLAB is presented at conferences, meetings and exhibitions throughout the world. Feel free to stop by our booth and speak to any of our representatives and receive an on-the-spot demo of models of your choice. For a list of other upcoming conferences visit: www.comsol.com/activities/events.

>>

>>


at these upcoming conferences:

2004 Fuel Cell Seminar Conference


UNRAVELING

more familiar with one package than another and so had no prejudices. Second, choose the benchmark problems carefully—they should be solvable and also challenge the code. Third, perform the benchmarks the same way sci-entists approach real-world problems. Fourth and finally, report the methods clearly enough to enable anyone to reproduce and verify the results. How to choose the benchmark problems is a study in itself, but highlights can be discussed here. One must find problems that are possible to set up in each program, problems where no one package had an obvious advan-tage. Everything—constants, lengths, materials and meth-ods—must be identical. According to Verdier, a major challenge is setting up the benchmarks such that you are solving the same problem even when working in different environments. Of course, there must be an objective basis for evaluating results, such as an analytic solution or wide-ly accepted and well documented results. In the benchmark analyses discussed here, test prob-lems were selected from classic texts and publications of standardizing agencies like NAFEMS (National Agency for Finite Element Methods and Standards). In other cases, the reviewers simply picked up sample problems from the manual sets of the packages being compared.

COMPARING MODEL PERFORMANCE

As important to reporting the benchmark results is proper-ly disclosing analysis particulars and addressing systematic differences between the testing committees. The following table gives such a summary for the FEMLAB-Fluent-Ansys comparisons.

Recently conducted benchmark studies answer some of these questions. In this article we recognize two recent projects that rank the performance of FEMLAB against two other leading products, Ansys and Fluent. One study, writ-ten by Olivier Verdier at the Lund Institute of Technology (Ref 1), looks at all three packages. The other, by Michael Hanke at the Royal Institute of Technology (Ref 2), looks only at FEMLAB and Fluent. Because both studies are available for downloading (see URLs in the References), this article does not repeat their findings but instead exam-ines some of the issues these researchers faced, along with selected benchmark results. Considering that FEMLAB is a general-purpose PDE solver capable of addressing an unusually wide range of problems, we are particularly interested for you to see how it ranks next to Ansys and Fluent, which are optimized for specific applications. In reviewing the benchmark studies please bear in mind the following questions: Can a gen-eral-purpose package perform as well as a task-specific one? Does flexibility demand you take a hit in performance?

ENSURING FAIR, HONEST COMPARISONS

At first glance it seems that benchmarking software should be straightforward, but the truth is a number of roadblocks must be smoothed over to ensure that the tests are honest and fair. There are four overarching responsibilities of the testers. First, become equally acquainted with the underly-ing operating philosophy of each package before the test-ing. In this regard, Verdier believes it was a benefit that he had never used any of these packages before. He was no

As the table shows, both Verdier and Hanke ran the test programs on a 2.4-GHz Pentium 4 machine with 1 Gbyte of RAM but used different operating systems: Verdier per-formed his tests under Windows XP, whereas Hanke ran them with SuSE Linux 8.1 (kernel 2.4.21-SuSE). To compare performance between the programs, a test problem was solved to a prescribed accuracy, and the memory consumption and execution time required to meet that accuracy were measured using tools provided on the machines. With the Windows Task manager, Ver-dier recorded program execution and memory consump-tion. With his Linux machine, Hanke recorded program execution time using the system’s real-time clock (script access). To report on memory consumption, he chose an indirect measure, the time the programs started to swap memory. The need for the indirect measure arose due to multithreading with Linux. He considered a model size to be computable if the process did not start to swap. Another variable in the formulae was tuning of the solver settings. Neither Hanke nor Verdier tried to tailor these parameters for maximum performance and instead used standard settings as much as possible. Hanke did make one exception to equalize test conditions. The ter-mination criterion for the nonlinear iteration is based on scaled error estimation in FEMLAB and a scaled residual in Fluent. To put the solvers on an equal footing, he de-creased the tolerance in Fluent to the same one used in FEMLAB (10 –6). As a final challenge, Verdier artificially increased the number of degrees of freedom, as he felt this would make the tests more meaningful. For example, in a structural-mechanics benchmark dealing with an elliptic membrane, a few thousand DOFs suffice to solve the problem, but then it is difficult to see major differences between the programs because they execute such a small problem rather quickly, in a matter of seconds. “It’s mandatory to use big problems if the tests are to be meaningful and accurate,” comments Verdier. “People aren’t really interested in test cases that use only a few degrees of freedom.” He increased the mod-el to use almost 100,000 DOFs to “stress” the problems. As you can see from the selected benchmark results shown here, a general-purpose modeling package can meet speed and accuracy standards set by single-physics packages.

References

1. Verdier, Oliver, “Benchmark of FEMLAB, Fluent and ANSYS”, Lund Institute of Technology, Centre for Mathemati-cal Sciences and Numerical Analysis www.maths.lth.se/na/staff/olivier/BenchmarkReport2.pdf 2. Hanke, Michael, “Benchmarking FEMLAB 3.0a: Laminar Flows in 2D and 3D”, Royal Institute of Technology (Stockholm), Department of Numerical Analysis and Computer Science, Parallel and Scientific Computing Institute.www.psci.kth.se/Activities/Reports/Results/2004/benchm.pdf

SELECTED BENCHMARK RESULTS

The following tables give an overview of selected results from the benchmark studies. They

present the accuracy figure as the negative logarithm of the relative deviation from a refer-

ence value—the higher value, the better the accuracy. An accuracy value of 1.0 corresponds

to 90% of the exact value; a value of 2.0 equals 99%, 3.0 equals 99.9%, and so on.

Structural Mechanics: Elliptic membrane; linear elastic analysis of stress in the y-direction

Structural Mechanics: Built-in plate; linear elastic analysis of displacement and principal stress

Fluid Dynamics: Laminar flow around a cylinder in 2D. The cylinder is slightly offset from the center of the channel. This results in a lifting force, measured as the lift coefficient. The drag force of the cylinder is measured as the drag coefficient.

A nice thing about buying scientific software is the short break-even time: a new package typically pays off within a job or two. Still there are a few things to consider. Will the package handle my problem? Will it provide accurate results? Does it operate fast enough? Is it straightforward to use, or should we allocate funds for consulting? Over the useful life of a package, these issues can result in expenses or savings far beyond the initial outlay.

a benchmark studyBY PAUL SCHREIER, ED FONTES & LE IGH SOUTTER

VERDIER (2004) HANKE (2004)

Packages examined FEMLAB, Fluent, Ansys FEMLAB, Fluent

Hardware 2.4-GHz Pentium 4 machine 2.4-GHz Pentium 4 machine

with 1 Gbyte of RAM with 1 Gbyte of RAM

Operating system Windows XP Linux 8.1 (kernel 2.4.21-SuSE)

Execution time Windows Task Manager Real-time clock

Memory consumption Direct-Windows Task Manager Indirect-swap time

Solver settings Default Default except Fluent error

tolerance reduced to that

of FEMLAB

Additional challenge Increased degrees of freedom None

Y-direction Number of DOF Peak Memory CPU time StressProgram (thousands) (MB) (seconds) Accuracy

Ansys 7.1 74 180 10 2.67

FEMLAB 3.0a 76 135 9 3.12

Principal Number of DOF Peak Memory CPU time Displacement StressProgram (thousands) (MB) (seconds) Accuracy Accuracy

Ansys 7.1 101 547 72 1.22 1.05

FEMLAB 3.0a 101 309 85 1.38 1.07

Drag Lift Number of DOF Peak Memory CPU time Coefficient CoefficientProgram (thousands) (MB) (seconds) Accuracy Accuracy

Fluent 6.1.18 109 67 450 1.97 < 1

FEMLAB 3.0a 101 371 108 4.75 2.13


2005

DenmarkCOMSOL A/SRosenkæret 11CDK-2860 SøborgPhone: +45 39 66 56 50Fax: +45 39 66 56 [email protected]

FinlandCOMSOL OYLauttasaarentie 52FIN-00200 HelsinkiPhone: +358 9 2510 400Fax: +358 9 2510 [email protected] www.comsol.fi

FranceCOMSOL France19 rue des bergersF-38000 GrenoblePhone: +33 (0)4 76 46 49 01Fax: +33 (0)4 76 46 07 [email protected]

GermanyFEMLAB GmbHBerliner Str. 4D-37073 GöttingenPhone: +49-551-99721-0Fax: [email protected]

NorwayCOMSOL ASVerftsgata 4NO-7485 TrondheimPhone: +47 73 84 24 00Fax: +47 73 84 24 [email protected]

SwedenCOMSOL ABTegnérgatan 23SE-111 40 StockholmPhone: +46 8 412 95 00Fax: +46 8 412 95 [email protected]

United KingdomCOMSOL Ltd.John Eccles HouseRobert Robinson AvenueThe Oxford Science ParkOxford OX4 4GPPhone: +44-1865-338-036Fax: [email protected]

United States COMSOL, Inc.8 New England Executive ParkSuite 310Burlington, MA 01803Phone: +1-781-273-3322Fax: [email protected]

COMSOL, Inc.1100 Glendon Avenue 17th FloorLos Angeles, CA 90024Phone: +1-310-689-7250Fax: [email protected]

W O R L D W I D E C O M S O L O F F I C E S

These FEMLAB Conferences are superbowls for FEMLAB users—defi nitely

the places to be to explore the cutting edge in multiphysics modeling. The

conferences offer you unique opportunities to meet with your colleagues,

get inspired by keynote speakers, and participate in hands-on tours through

new software innovations by FEMLAB experts. Consider the possibilities—

researchers from all fi elds will present a host of new models, and all of them

will be built on the same code you use everyday.

THEY ARE HELD WORLDWIDE FALL 2005The FEMLAB Conferences are coming to you. FEMLAB teams around the world will set up full two-day conferences as well as condensed one-day events packed with learning and networking opportunities.

VENUES

• BOSTON

• COPENHAGEN

• FRANKFURT

• HELSINKI

• LONDON

• PARIS

• STOCKHOLM

• TRONDHEIM

CALL FOR PAPERS

Do you have an application in engineering, research or education that you would like to share with your colleagues? If so, you are warmly welcome to submit an abstract for presentation at the FEMLAB Conference 2005. Suggested topics:

• Microwave engineering

• Optics

• Photonics

• Porous media fl ow

• Quantum mechanics

• Radio-frequency components

• Semiconductor devices

• Structural mechanics

• Transport phenomena

• Wave propagation.

• Acoustics

• Bioscience

• Chemical reactions

• Diffusion

• Electromagnetics

• Fluid dynamics

• Fuel cells

• Geophysics

• Heat transfer

• Micro-electromechanical

systems (MEMS)

Send an e-mail to [email protected] to give an early notice of which topic you would like to submit a paper on.

For international representatives visit www.comsol.com/contact/offi ces.php

Do you want to view your colleague s

FEMLAB models?

FEMLAB is a registered trademark of COMSOL AB.

– brings you FEMLAB

OTHER FREE OFFERS!2004 Spring Tour CD–this CD contains FEMLAB presentations, animations, model documentation and FEMLAB fi les from our worldwide seminar tour this past spring. Visit www.comsol.com/tourcd.

2004 User Presentation CD–this CD is a unique collection of models developed by FEMLAB users at companies and universities around the world. Go to www.comsol.com/usercd.

Then get your free FEMLAB Multiphysics Viewer. This Viewer lets you or your colleagues view and postprocess FEMLAB 3 models on any computer running Windows, Linux, or Macintosh systems. Click on www.comsol.com/viewerto receive the software on CD. It is totally free of charge!

2 4 C O M S O L N E W S V O L . 1 2 0 0 4

In the 1970´s and 1980´s I wrote finite element code for the Navier-Stokes equations and extensions, but I could only involve graduate students because of the complexity of the code and the debugging limitations of FORTRAN. As soon as Matlab was available I had undergraduate students and graduate students using its ODE solvers to solve initial value problems, and, with some help from the finite difference method,

partial differential equations in one dimension. Elliptic boundary value problems, though, were inaccessible (without a lot of programming) until COMSOL developed the PDE Toolbox to run on top of Matlab. The graphical user interface allowed easy solution of Laplace’s equation and variants in complicated geometries. I had to reinvent myself, at least my teaching style. I created a one-page handout describing the steps one used to setup the problem (draw, mesh, subdomain parameters, boundary conditions, solve, plot). By demonstrating the program in class, and having the one-page handout, students were able to use the PDE Toolbox with ease. I wanted to do the same thing with the Navier-Stokes equations, since it is used so widely in chemical engineering. But, alas, the only options were

By Bruce A. FinlaysonRehnberg Professor of Chemical Engineering, University of Washington

A Professor’s Dream Fulfilled

commercial codes that were not very user friendly. While my graduate students could learn to use them, undergraduates and students in graduate classes needed too much hand-holding to use them extensively beyond the model problems. Thus, I stopped my campaign to teach all students about the finite-element method for the Navier-Stokes equations despite the flow situations they encounter. When FEMLAB 1.0 came out, a visiting student from Thailand came and asked me if she could do an undergraduate research project with me. I dreamed one up, and we eagerly awaited the first version. It didn’t arrive until half the quarter was gone, but she had learned to use the PDE Toolbox and it was a simple step to use FEMLAB. She did excellent work with 2D flows, and even taught me something. It was then that I had to reinvent myself again! I had learned that undergraduates could solve the Navier-Stokes equations in complicated geometries and obtain useful results, and it didn’t require my constant attention to do so. As FEMLAB has improved to its current version 3 (sometimes with suggestions from our teams), we’ve expanded the scope of problems we solve. The focus is on microfluidics, and the pressure drop, mixing, and dispersion in 2D and 3D. Earlier versions had memory and convergence problems, but COMSOL engineers helped us over those rough spots, and now these are less of a problem. The undergraduates are co-authors of publications, and they learn to do research with the latest tools. My goal now is to get them to recognize that the whole solution is not the pretty, colorful pictures, but the details that are easily obtained in FEMLAB. All told, in the past three years I directed over 20 undergraduate researchers to complete meaningful projects based on sophisticated flow calculations. This would only have been possible with FEMLAB.

Follow this link to some of Dr. Finlayson’s FEMLAB assignments:

faculty.washington.edu/finlayso

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COMSOL News 2004 · The focus of this fi rst issue of COMSOL News is multiphysics modeling. Consider that a typical problem in the area of MEMS (microelectromechanical systems) requires