# Second-order transmission conditions for the Helmholtz equation

@inproceedings{Douglas1997SecondorderTC, title={Second-order transmission conditions for the Helmholtz equation}, author={Jim Douglas and Douglas B. Meade}, year={1997} }

We present an iterative nonoverlapping domain decomposition method with second-order Robin-type transmission conditions for the scalar Helmholtz equation in two dimensions. The analysis of the proposed method parallels that for the traditional Robin-type transmission conditions. The new method requires no additional computational complexity and exhibit a more rapid convergence to the exact solution.

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## 6 Citations

Absorbing boundary conditions for the wave equation and parallel computing

- Mathematics, Computer ScienceMath. Comput.
- 2005

The authors optimize the absorbing boundary conditions in domain decomposition algorithms for the wave equation in order to obtain a good performance of the Schwarz waveform relaxation algorithm.

17. New Interface Conditions for Non-overlapping Domain Decomposition Iterative Procedures

- Computer Science
- 2001

This analysis covers Seidel-type schemes for a general class of problems, such as elliptic, Helmholtz, Maxwell, and elasticity problems, etc, which is entirely independent of the governing model problems of a specific type of partial differential equations.

A Class of Iterative Solvers for the Helmholtz Equation: Factorizations, Sweeping Preconditioners, Source Transfer, Single Layer Potentials, Polarized Traces, and Optimized Schwarz Methods

- Mathematics, Computer ScienceSIAM Rev.
- 2019

The goal of the present manuscript is to show that this class of preconditioners developed by researchers with various backgrounds are based on a common mathematical principle, and they can all be formulated in the context of domain decomposition methods called optimized Schwarz methods.

Additive Schwarz Methods with Nonre ecting Boundary Conditions for the Parallel Computation of Helmholtz Problems

- 1998

Recent advances in discretizations and preconditioners for solving the exterior Helmholtz problem are combined in a single code and their bene ts evaluated on a parameterized model. Motivated by…

A fast algorithm based on partial basic solution vectors domain decomposition method for scattering analysis of electrically large cylinders

- Mathematics, Computer ScienceJ. Comput. Phys.
- 2006

An efficient domain decomposition method based on the partial basic solution vectors (PBSV) is presented for the electromagnetic scattering analysis of electrically large two-dimensional objects and can greatly reduce the computational complexity and the memory requirement.

A diagonal sweeping domain decomposition method with source transfer for the Helmholtz equation

- Mathematics, Computer ScienceCommunications in Computational Physics
- 2021

It is proved that the exact solution is obtained with the proposed method in the constant medium case, and also in the two-layered medium case provided the source is on the same side with the first swept subdomain.

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