• Corpus ID: 6282109

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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References

SHOWING 1-10 OF 44 REFERENCES
A Domain Decomposition Method for the Helmholtz Equation and Related Optimal Control Problems
We present an iterative domain decomposition method to solve the Helmholtz equation and related optimal control problems. The proof of convergence of this method relies on energy techniques. This
The construction of preconditioners for elliptic problems by substructuring. I
In earlier parts of this series of papers, we constructed preconditioners for the discrete systems of equations arising from the numerical approximation of elliptic boundary value problems. The
COMPARISON OF TWO-DIMENSIONAL CONFORMAL LOCAL RADIATION BOUNDARY CONDITIONS
Numerical solutions for open-region electromagnetic problems based on differential equations require some means of truncating the computational domain. A number of local Radiation Boundary Conditions
Numerical Experiments on a Domain Decomposition Algorithm for Nonlinear Elliptic Boundary Value Problems
In this note we present numerical experiments on a domain decomposition algorithm for nonlinear elliptic boundary value problems in planar domains. There has recently been much progress in the
A domain decomposition method for the optimal DOUGLAS & MEADE control of systems governed by the Helmholtz equation
  • Mathematical and Numerical Aspects of Wave Propagation Phenomena
  • 1995
A domain decomposition method for the optimal control of systems governed by the Helmholtz equation
  • Mathematical and Numerical Aspects of Wave Propagation Phenomena
  • 1995
A domain decomposition method for the optimal control of systems governed by the Helmholtz equation
  • Mathematical and Numerical Aspects of Wave Propagation Phenomena
  • 1995
An non-overlapping iterative linear domain decomposition method for the Helmholtz problem
  • An non-overlapping iterative linear domain decomposition method for the Helmholtz problem
  • 1995
An non-overlapping iterative linear domain decomposition method for the Helmholtz problem
  • An non-overlapping iterative linear domain decomposition method for the Helmholtz problem
  • 1995
Domain de omposition method for harmoni wave equations
  • 1995
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