Fast algorithms for the solution of scattering problems
by Boundary Element Methods

AMS-304: 2019/2020

Topics

    • Boundary Element Methods for scattering problems
    • Fast modern algorithms: motivation, complexity analysis and principle
    • Principle of low-rank approximations: Singular Value Decomposition and Adaptive Cross Approximation
    • Fast Algebraic Solvers: Hierarchical Matrices
    • Fast Multipole Methods: principle for particles, FMM for Helmholtz

Lecture Materials

    • Note de Conseils pour les comptes-rendus de TPs: [Pdf]
    • Session 1: Introduction [Pdf] / Theory: Fundamental solutions and Boundary Integral Representation (E. Becache)
    • Session 2: TP on Boundary Integral Representation [Pdf TP] / Theory: Boundary Integral Representation (E. Becache)
    • Session 3: TP on Boundary Integral Representation [Aide TP]
    • Session 4:TP on Boundary Integral Representation/ Theory: Boundary Integral Equations [Poly]
    • Session 5: How to deal with singular integrals/ TP on Boundary Integral Equations [Pdf TP]
    • Session 6: TP on Boundary Integral Equations
    • Session 7: Fast algebraix BEMs [Pdf]/ TP on low rank approximations [Pdf TP]
    • Session 8: Fast algebraix BEMs [Pdf ]/ TP on Hierarchical matrices
    • Session 9: TP on Hierarchical matrices
    • Session 10: Presentation of the 3 TPs