Generalized Dirichlet to Neumann map for moving initial-boundary value problems

The generalised Dirichlet to Neumann map for moving initial-boundary value problems

We present an algorithm for characterising the generalised Dirichlet to Neumann map for moving initial-boundary value problems. This algorithm is derived by combining the so-called global relation, which couples the initial and boundary values of the problem, with a new method for inverting certain one-dimensional integrals. This new method is based on the spectral analysis of an associated ODE...

Dirichlet-to-neumann Boundary Conditions for Multiple Scattering Problems

A Dirichlet-to-Neumann (DtN) condition is derived for the numerical solution of time-harmonic multiple scattering problems, where the scatterer consists of several disjoint components. It is obtained by combining contributions from multiple purely outgoing wave fields. The DtN condition yields an exact nonreflecting boundary condition for the situation, where the computational domain and its ex...

Generalized BSDEs and nonlinear Neumann boundary value problems

We study a new class of backward stochastic di€erential equations, which involves the integral with respect to a continuous increasing process. This allows us to give a probabilistic formula for solutions of semilinear partial di€erential equations with Neumann boundary condition, where the boundary condition itself is nonlinear. We consider both parabolic and elliptic equations.

Müntz-Galerkin Methods and Applications to Mixed Dirichlet-Neumann Boundary Value Problems

Solutions for many problems of interest exhibit singular behaviors at domain corners or points where boundary condition changes type. For this type of problems, direct spectral methods with usual polynomial basis functions do not lead to a satisfactory convergence rate. We develop in this paper a Müntz-Galerkin method which is based on specially tuned Müntz polynomials to deal with the singular...

Approximating Initial-Value Problems with Two-Point Boundary-Value Problems: BBM-Equation