Edith Frisk Gärtner: Fast evaluation of layer and volume potentials for the modified Helmholtz equation

Speaker:
Edith Frisk Gärtner, KTH Royal Institute of Technology

Abstract
We present a numerical method for solving the modified Helmholtz equation in complex geometries using potential theory. The solution is represented as a combination of a volume integral, accounting for the source distribution within the domain, and a boundary integral equation enforcing the prescribed boundary conditions. Layer and volume potentials are evaluated efficiently through an Ewald-type decomposition, in which the potential is split into a rapidly decaying local part, treated via asymptotic expansions, and a smooth history part computed using the nonuniform fast Fourier transform (NUFFT). The method is robust with respect to mesh imperfections, including degenerate triangles, large aspect ratios, and small geometric gaps. Numerical experiments demonstrate high accuracy across a range of parameters and geometries.