A general three-dimensional elliptic grid generation system on a composite block structure
Computer Methods in Applied Mechanics and Engineering
Non-reflecting boundary conditions
Journal of Computational Physics
A finite element/spectral method for approximating the time-harmonic Maxwell system in R3
SIAM Journal on Applied Mathematics
On nonreflecting boundary conditions
Journal of Computational Physics
A Finite-Element Method for Laplace- and Helmholtz-Type Boundary Value Problems with Singularities
SIAM Journal on Numerical Analysis
Numerical solution of problems on unbounded domains. a review
Applied Numerical Mathematics - Special issue on absorbing boundary conditions
Dirichlet-to-Neumann boundary conditions for multiple scattering problems
Journal of Computational Physics
Finite Differences And Partial Differential Equations
Finite Differences And Partial Differential Equations
High-order compact finite-difference methods on general overset grids
Journal of Computational Physics
Generation of curvilinear coordinates on multiply connected regions with boundary singularities
Journal of Computational Physics
Journal of Computational Physics
Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-Dependent Problems (Classics in Applied Mathematics Classics in Applied Mathemat)
Local absorbing boundary conditions for elliptical shaped boundaries
Journal of Computational Physics
Generation of smooth grids with line control for scattering from multiple obstacles
Mathematics and Computers in Simulation
Exact non-reflecting boundary conditions
Journal of Computational Physics
Journal of Computational and Applied Mathematics
Local nonreflecting boundary condition for time-dependent multiple scattering
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.47 |
The applicability of the Dirichlet-to-Neumann technique coupled with finite difference methods is enhanced by extending it to multiple scattering from obstacles of arbitrary shape. The original boundary value problem (BVP) for the multiple scattering problem is reformulated as an interface BVP. A heterogenous medium with variable physical properties in the vicinity of the obstacles is considered. A rigorous proof of the equivalence between these two problems for smooth interfaces in two and three dimensions for any finite number of obstacles is given. The problem is written in terms of generalized curvilinear coordinates inside the computational region. Then, novel elliptic grids conforming to complex geometrical configurations of several two-dimensional obstacles are constructed and approximations of the scattered field supported by them are obtained. The numerical method developed is validated by comparing the approximate and exact far-field patterns for the scattering from two circular obstacles. In this case, for a second order finite difference scheme, a second order convergence of the numerical solution to the exact solution is easily verified.