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Sweeping Preconditioner for the Helmholtz Equation:Hierarchical Matrix Representation
Sweeping Preconditioner Helmholtz Equation Hierarchical Matrix Representation
2015/7/14
The paper introduces the sweeping preconditioner, which is highly efficient for iterative solutions of the variable-coefficient Helmholtz equation including veryhigh-frequency problems. The first cent...
SWEEPING PRECONDITIONER FOR THE HELMHOLTZ EQUATION: MOVING PERFECTLY MATCHED LAYERS
Helmholtz equation perfectly matched layers high frequency waves preconditioners LDLt factorization Green’s function multifrontal methods optimal ordering
2015/7/14
This paper introduces a new sweeping preconditioner for the iterative solution of the variable coefficient Helmholtz equation in two and three dimensions. The algorithms follow the general structure o...
Additive Sweeping Preconditioner for the Helmholtz Equation
Helmholtz equation perfectly matched layers preconditioners high frequency waves
2015/7/14
We introduce a new additive sweeping preconditioner for the Helmholtz equation based on the perfect matched layer (PML). This method divides the domain of interest into thin layers and proposes a new ...
Recursive Sweeping Preconditioner for the 3D Helmholtz Equation
Helmholtz equation perfectly matched layers preconditioners high frequency waves
2015/7/14
This paper introduces the recursive sweeping preconditioner for the numerical solution of the Helmholtz equation in 3D. This is based on the earlier work of the sweeping preconditioner with the moving...
The Best Finite-Difference Scheme for the Helmholtz Equation
The Best Finite-Difference Scheme for the Helmholtz and Laplace’s Equations
2013/1/30
The best finite-difference scheme for the Helmholtz equation is suggested. A method of solving obtained finite-difference scheme is developed. The efficiency and accuracy of method were tested on seve...
Tikhonov regularization method for a Cauchy problem for the Helmholtz equation in multiple dimensions-----
inverse problems Helmholtz equation Tikhonov regularization error estimate
2011/10/18
This paper deals with a Cauchy problem for the Helmholtz equa- tion in multiple dimensions.We want to obtain the solution u on the boundary z = 0 from the given function g ontheside z = 1. This proble...
$L^p$-$L^q$ estimates for Electromagnetic Helmholtz equation
Electromagnetic Helmholtz equation math
2010/11/9
In space dimension $n\geq3$, we consider the electromagnetic Schr\"odinger Hamiltonian $H=(\nabla-iA(x))^2-V$ and the corresponding Helmholtz equation $(\nabla-iA(x))^2u+u-V(x)u=f \in \mathbb{R}^n$. ...
Two dimensional invisibility cloaking for Helmholtz equation and non-local boundary conditions
Two dimensional Helmholtz equation non-local boundary conditions
2010/11/15
Transformation optics constructions have allowed the design of cloaking devices that steer electromagnetic, acoustic and quantum waves around a region without penetrating it, so that this region is hi...
PIRINCIPLES OF RADIATION FOR HELMHOLTZ EQUATION IN N-DIMENSIONAL LAYER WITH IMPEDENCE BOUNDARY CONDITIONS
HELMHOLTZ EQUATION BOUNDARY CONDITIONS N-DIMENSIONAL LAYER
2010/3/17
The principle of limit absorption and A. G. Sveshnikov's partial conditions of radition for Helmholts equation in multile dimensinal layer with impedance boundary conditions were studied. The behavior...