Second kind boundary integral equation for multi-subdomain diffusion problems
The authors are concerned with the linear second-order diffusion problem for a given excitation field at infinity, harmonic on all of real 3D space. They restrict to piecewise constant real-valued diffusion coefficients. Then, they precisely describe the geometry and the boundary value problem, review basic definitions and results related to Sobolev spaces, introduce a functional framework well adapted to dealing with trace functions in a multi-subdomain context and establish the well-posedness of a variational formulation for the original problem. The corresponding trial functions are sought in single-trace spaces, and the test functions are chosen in some complementary subspace. Subsequently they rewrite this formulation in order to simplify the functional framework and carry out two numerical experiments. The Galerkin boundary element method applied to their new integral equations provides competitive results compared to the more classical first kind approach.
piecewise constant diffusion coefficient
scientific article; zbMATH DE number 6816265
scientific article