Surface Partial Differential Equations and its Applications to Scattering Problems

Curved spaces, such as surfaces, provide a rich setting for the study of partial differential equations (PDEs). Building upon the extensive research conducted on PDEs in flat spaces, the extension of these equations to curved spaces has garnered considerable attention in the field of mathematics. One prominent example is the Laplace Beltrami equation. In this work, we employ efficient direct solvers to obtain solutions for PDEs on surfaces and demonstrate their applicability in solving conventional electromagnetic scattering problems.