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Parallelisation of Nonlinear Structural Analysis using Dual Partition Super-Elements G.A. Jokhio and B.A. Izzuddin

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Overview Introduction Proposed Structural Decomposition Approach Implementation by Parallelisation Verification Conclusions

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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

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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

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Introduction Implementation Parallelisation of ADAPTIC MPI Verification Examples

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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) 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)

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2 nd Level of Partitioning 1 st Level of Partitioning Structural Domain Partitioning Hierarchical Approach Partition super element on parent side Dual partition super element on child side

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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

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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

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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

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Implementation Start, Initialize MPI Send Load Factor, Incremental Displacements etc. to the Partitions` Get Resistance Forces and Tangent Stiffness from the Partitions Check Convergence Next Iteration or Load Step? End Overview of the Parent Structure Algorithm

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Implementation Start, Initialize MPI Receive Instruction and the relevant data from the Parent Overview of the Partition/Child Algorithm Perform the relevant Task Continue? End Send the Outcome of the relevant task to the parent

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Verification Example 1: A 4 storey Structure 6 3 3 3 4 3 3 3 4 6 Original StructurePartition No. 1 Partition No. 2 Node 42 x y Parent Structure

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Verification Example 2: I-Beam using 3D Brick Elements Time taken for monolithic analysis188 seconds Time taken for partitioned analysis with 3 partitions 80 seconds Time saved57.4 %

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Verification Example 3: 3D Framed Structure Load steps completed (in 72 hours) for: Initial LoadingTime-historyTotal Monolithic analysis 1910 Partitioned analysis with 11 partitions 1120121

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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

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Acknowledgements Higher Education Commission of Pakistan High Performance Computing (HPC) Services, Imperial College London

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