Parallelisation of Nonlinear Structural Analysis using Dual Partition Super-Elements

G.A. Jokhio and B.A. Izzuddin

Overview

•Introduction

•Proposed Structural Decomposition Approach

•Implementation by Parallelisation

•Verification

•Conclusions

Introduction

• A new approach of structural domain partitioning

• Parts of a structure replaced by partition super elements

• Removed parts modelled separately as child structures

• Dual partition super elements wrap the partition boundary of respective

child structures

Introduction

Purpose

• Reduction in computational time

• By using parallel processing

• By using reduced dimensional elements for non-critical parts

• Simplification of modelling

• By modular modelling

• Freedom

• To choose partitions

• To use different integration schemes

• To consider multi-physics

Introduction

•Implementation

• Parallelisation of ADAPTIC

• MPI

•Verification Examples

Case 2: A parent and a child partition (parent also models a part of structure made with other elements)

Case 2: A parent and a child partition (parent also models a part of structure made with other elements)

Case 3: A parent and a child partition (Same as case 2 but parent and child roles reversed)

Case 3: A parent and a child partition (Same as case 2 but parent and child roles reversed)

Structural Domain Partitioning

Partition super element on parent side

Dual partition super element on child side

Case 1: A parent and 2 child partitions (parent has only partition super elements)

Case 1: A parent and 2 child partitions (parent has only partition super elements)

2nd Level of Partitioning2nd Level of Partitioning1st Level of Partitioning1st Level of Partitioning

Structural Domain Partitioning

Hierarchical Approach

Partition super element on parent side

Dual partition super element on child side

Rationale

• Partitions ‘represented’ by partition super elements

• Any solution procedure based on monolithic approach ‘will do’

• The child partition boundary is analogous to Essential Boundary Conditions

• Compatibility: Parent sends these BCs to partitions

• Equilibrium: Parent receives the tangent stiffness and resistance forces from

partitions

Procedure

•Load/Time Steps

• Step wise loading/time-stepping controlled by the parent

• The load factor/time is sent to the partitions

•Equilibrium Convergence

• Convergence at parent structure level

• Convergence at partition level

•Iteration

• Iterative corrections to displacements sent to the partitions

• Resulting forces and tangent stiffness received by the parent

•The Frontal Method is most suitable – other methods can be used

Implementation

ADAPTIC

• Source code available

• Written in Fortran – Most widely used language in HPC

• Analysis types:• Static Proportional Loading• Static Time History• Dynamic• Eigenvalue

• A wide range of structural elements and material models available

• Supports advanced adaptive techniques

Other structural analysis programs can

also be used

Implementation

Start, Initialize MPIStart, Initialize MPI

Send Load Factor, Incremental Displacements etc. to the

Partitions`

Send Load Factor, Incremental Displacements etc. to the

Partitions`

Get Resistance Forces and Tangent Stiffness from the

Partitions

Get Resistance Forces and Tangent Stiffness from the

Partitions

Check ConvergenceCheck Convergence

Next Iteration or Load Step?Next Iteration or Load Step?

EndEnd

Overview of the

Parent Structure

Algorithm

Implementation

Start, Initialize MPIStart, Initialize MPI

Receive Instruction and the relevant data from the ParentReceive Instruction and the

relevant data from the Parent

Overview of the

Partition/Child

Algorithm

Perform the relevant TaskPerform the relevant Task

Continue?Continue?

EndEnd

Send the Outcome of the relevant task to the parent

Send the Outcome of the relevant task to the parent

Verification

Example 1: A 4 storey Structure

6

3

3

3

4

3

3

3

4

6

Original Structure Partition No. 1 Partition No. 2

Node 42

x

y

Parent Structure

Verification

Example 2: I-Beam using 3D Brick Elements

Time taken for monolithic analysis 188 secondsTime taken for partitioned analysis with 3 partitions

80 seconds

Time saved 57.4 %

Verification

Example 3: 3D Framed Structure

Load steps completed (in 72 hours) for:

Initial Loading Time-history Total

Monolithic analysis

1 9 10

Partitioned analysis with 11 partitions

1 120 121

Conclusions

• A new structural decomposition approach for partitioned analysis using

parallel processing has been proposed

• Uses dual partition-super elements

• Can be used for the parallelisation of existing monolithic analysis codes

• Has been implemented with ADAPTIC using a parallel MPI scheme

• The results match exactly with those obtained from conventional

monolithic analysis

• Significant computational savings arise in the analysis of large structures,

with great speedups achieved

• The proposed partitioning approach can also simplify the modelling

process through the use of modular partitions

Acknowledgements

• Higher Education Commission of Pakistan

• High Performance Computing (HPC) Services, Imperial College London

Questions?