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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

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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)

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

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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

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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

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.....

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.....

.

Context Problem Formulation Matrix Approach FMM Approach Conclusion & Perspectives

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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

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Context Problem Formulation Matrix Approach FMM Approach Conclusion & Perspectives

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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

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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, ...

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Context Problem Formulation Matrix Approach FMM Approach Conclusion & Perspectives

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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, ...

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.

Context Problem Formulation Matrix Approach FMM Approach Conclusion & Perspectives

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Outline

Problem Formulation

BEM Solver (Matrix Approach)

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

Conclusion & Perspectives

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Context Problem Formulation Matrix Approach FMM Approach Conclusion & Perspectives

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TD-BEM Application Stages

User inputs, simulation parameters

Mesh generator, configuration

Solver

Post-processing (TD FD)

Optimiza

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