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  • Optimization and Parallelization of the BoundaryElement Method for the Wave Equation

    in Time Domain

    Berenger Bramas

    Inria, Bordeaux - Sud-Ouest

    PhD defense - Feb. 15th 2016

    Advisor: Oliver Coulaud (Inria)

    Industrial co-advisor: Guillaume Sylvand (Airbus)

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    Context Problem Formulation Matrix Approach FMM Approach Conclusion & Perspectives

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    Context

    Optimization and Parallelization of the Boundary Element Method for the Wave Equation in Time Domain Berenger Bramas

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    Context Problem Formulation Matrix Approach FMM Approach Conclusion & Perspectives

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    Wave Equation Problems

    Study the wave propagation in acoustics or electromagnetism Critical in several industrial fields (design, robustness study)

    In our case: antenna placement, electromagnetic compatibility,furtivity, lightning, ...

    Image from Airbus Group.

    Optimization and Parallelization of the Boundary Element Method for the Wave Equation in Time Domain Berenger Bramas

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    Context Problem Formulation Matrix Approach FMM Approach Conclusion & Perspectives

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    Wave Equation Simulations

    Boundary element method (BEM): integral equation over adiscretized mesh

    Interest of BEM compared to other approaches

    Better accuracy Surfacic mesh (easier to produce)

    Disadvantages of BEM

    Dense matrices (specific solvers)

    Optimization and Parallelization of the Boundary Element Method for the Wave Equation in Time Domain Berenger Bramas

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    Context Problem Formulation Matrix Approach FMM Approach Conclusion & Perspectives

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    BEM

    Boundary Element Method (BEM) for the Wave Equation

    In Time Domain (TD) In Frequency Domain (FD)

    One solve = a range of frequencies(Fourier Transform)

    One solve = one frequency

    Advantages/disadvantages depend on the application/configuration

    Optimization and Parallelization of the Boundary Element Method for the Wave Equation in Time Domain Berenger Bramas

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    Context Problem Formulation Matrix Approach FMM Approach Conclusion & Perspectives

    (5)

    BEM

    Boundary Element Method (BEM) for the Wave Equation

    In Time Domain (TD) In Frequency Domain (FD)

    Accelerated by FMM (Fast-BEM)

    Accelerated by H-Matrix

    Accelerated by FMM

    Dense BEM/Matrix Approach Dense BEM

    ......

    One solve = a range of frequencies One solve = one frequency

    Advantages/disadvantages depend on the application/configuration

    Optimization and Parallelization of the Boundary Element Method for the Wave Equation in Time Domain Berenger Bramas

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    Context Problem Formulation Matrix Approach FMM Approach Conclusion & Perspectives

    (5)

    BEM

    Boundary Element Method (BEM) for the Wave Equation

    In Time Domain (TD) In Frequency Domain (FD)

    Accelerated by FMM (Fast-BEM)

    Accelerated by H-Matrix

    Accelerated by FMM

    Dense BEM/Matrix Approach Dense BEM

    ......

    One solve = a range of frequencies One solve = one frequency

    Less studied and used Widely used (academy and industry)

    Advantages/disadvantages depend on the application/configuration

    Optimization and Parallelization of the Boundary Element Method for the Wave Equation in Time Domain Berenger Bramas

  • ..........

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    ......

    .....

    .....

    .

    Context Problem Formulation Matrix Approach FMM Approach Conclusion & Perspectives

    (5)

    BEM

    Boundary Element Method (BEM) for the Wave Equation

    In Time Domain (TD) In Frequency Domain (FD)

    Accelerated by FMM (Fast-BEM)

    Accelerated by H-Matrix

    Accelerated by FMM

    Dense BEM/Matrix Approach Dense BEM

    ......

    One solve = a range of frequencies One solve = one frequency

    Less studied and used Widely used (academy and industry)

    Advantages/disadvantages depend on the application/configuration

    Optimization and Parallelization of the Boundary Element Method for the Wave Equation in Time Domain Berenger Bramas

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    Context Problem Formulation Matrix Approach FMM Approach Conclusion & Perspectives

    (6)

    Industrial Context

    In partnership with Airbus Group Innovation (financed jointlywith Region Aquitaine)

    Airbus solvers: FD-BEM

    Accelerated by FMM or H-Matrix techniques TD-BEM (experimental)

    No stability problem (formulation based on a full Galerkindiscretization unconditionnaly stable from [Terrasse, 1993])

    With FMM [Ergin et al., 2000] (trial)

    Objective:

    Reduce the performance gap between FD and TD approaches

    Optimization and Parallelization of the Boundary Element Method for the Wave Equation in Time Domain Berenger Bramas

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    .

    Context Problem Formulation Matrix Approach FMM Approach Conclusion & Perspectives

    (6)

    Industrial Context

    In partnership with Airbus Group Innovation (financed jointlywith Region Aquitaine)

    Airbus solvers: FD-BEM

    Accelerated by FMM or H-Matrix techniques TD-BEM (experimental)

    No stability problem (formulation based on a full Galerkindiscretization unconditionnaly stable from [Terrasse, 1993])

    With FMM [Ergin et al., 2000] (trial)

    Objective:

    Reduce the performance gap between FD and TD approaches

    Optimization and Parallelization of the Boundary Element Method for the Wave Equation in Time Domain Berenger Bramas

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    Context Problem Formulation Matrix Approach FMM Approach Conclusion & Perspectives

    (7)

    HPCSuper-computers are mandatory to solve large problems

    Shared/Distributed memory Heterogeneous (one or more GPU per node)

    CPU CPU

    GPU

    Node

    CPU CPU

    GPU

    Node

    CPU CPU

    GPU

    Node

    CPU CPU

    GPU

    Node

    ...

    Cluster

    Some of the challenges

    Efficient computational algorithm/kernel Parallelization Balancing Hardware abstraction, portable implementation, long-termdevelopment, ...

    Optimization and Parallelization of the Boundary Element Method for the Wave Equation in Time Domain Berenger Bramas

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    Context Problem Formulation Matrix Approach FMM Approach Conclusion & Perspectives

    (7)

    HPCSuper-computers are mandatory to solve large problems

    Shared/Distributed memory Heterogeneous (one or more GPU per node)

    CPU CPU

    GPU

    Node

    CPU CPU

    GPU

    Node

    CPU CPU

    GPU

    Node

    CPU CPU

    GPU

    Node

    ...

    Cluster

    Some of the challenges

    Efficient computational algorithm/kernel Parallelization Balancing Hardware abstraction, portable implementation, long-termdevelopment, ...

    Optimization and Parallelization of the Boundary Element Method for the Wave Equation in Time Domain Berenger Bramas

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    .

    Context Problem Formulation Matrix Approach FMM Approach Conclusion & Perspectives

    (8)

    Outline

    Problem Formulation

    BEM Solver (Matrix Approach)

    Fast-Multipole Method Approach FMM Algorithm & Parallelization FMM BEM Solver (Experimental Implementation)

    Conclusion & Perspectives

    Optimization and Parallelization of the Boundary Element Method for the Wave Equation in Time Domain Berenger Bramas

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    Context Problem Formulation Matrix Approach FMM Approach Conclusion & Perspectives

    (9)

    TD-BEM Application Stages

    User inputs, simulation parameters

    Mesh generator, configuration

    Solver

    Post-processing (TD FD)

    Optimiza

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