MTL888: Boundary Elements Methods with Computer Implementation

3 Credits (3-0-0)

Distributions and Sobolev spaces of fractional order. Elliptic boundary value problems on unbounded domains in IRn (n=2,3).

Fundamental solution of elliptic equations.

Simple layer and double layer potentials Fredholm integral equations of first and second kinds. Singular and hypersingular kernels.

Interior and exterior Dirichlet problems and integral representations of their solutions.

Variational formulation of problems defined on boundary. Solution of some model problems by boundary element methods, approximate integrations over boundary, solution methods of algebraic equations; computer implementation of boundary element methods for a model problem. Coupling of boundary element and finite element methods.

Some advanced topics of boundary integral methods integrals with hypersingular kernel, a method of elimination of singularity, Lagrange multiplier method.