Scientific Computing Seminar
Abstract: We begin with a brief and general description of the difference potentials method (DPM), emphasizing the opportunities that this methodology provides in the context of the following applications: - numerical solution of boundary value problems with complex boundary conditions; - transfer of boundary conditions from infinity to a finite artificial boundary; - DPM-based approach to domain decomposition and parallel computing; - finite-difference model for active shielding and noise control; We will then analyze some specific contrasts between the DPM and the general finite-difference method (FDM) and boundary element method (BEM), from the computational point of view. Finally, we will delineate the construction of difference potentials in the general setting, when the density of the potential belongs to the so-called space of jumps. The latter are analogous to the boundary discontinuities of the surface potentials for elliptic operators (e.g., double- and single-layer) in the classical potential theory.
<--- 1997 Index