Sweeping preconditioner for the Helmholtz equation: Hierarchical matrix representation
نویسندگان
چکیده
منابع مشابه
Sweeping Preconditioner for the Helmholtz Equation: Hierarchical Matrix Representation
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 central idea of this novel approach is to construct an approximate factorization of the discretized Helmholtz equation by sweeping the domain layer by layer, starting from an absorbing layer or boundar...
متن کاملAdditive Sweeping Preconditioner for the Helmholtz Equation
We introduce a new additive sweeping preconditioner for the Helmholtz equation based on the perfectly matched layer (PML). This method divides the domain of interest into thin layers and proposes a new transmission condition between the subdomains where the emphasis is on the boundary values of the intermediate waves. This approach can be viewed as an effective approximation of an additive deco...
متن کاملSweeping Preconditioner for the 3 D 1 Helmholtz Equation
This paper introduces the recursive sweeping preconditioner for the numerical solu4 tion of the Helmholtz equation in 3D. This is based on the earlier work of the sweeping preconditioner 5 with the moving perfectly matched layers (PMLs). The key idea is to apply the sweeping precondi6 tioner recursively to the quasi-2D auxiliary problems introduced in the 3D sweeping preconditioner. 7 Compared ...
متن کاملSweeping Preconditioner for the Helmholtz Equation: Moving Perfectly Matched Layers
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 of constructing an approximate LDLt factorization by eliminating the unknowns layer by layer starting from an absorbing layer or boundary condition. The central idea of this paper is to approximate ...
متن کاملRecursive Sweeping Preconditioner for the Three-Dimensional Helmholtz Equation
This paper introduces the recursive sweeping preconditioner for the numerical solution of the Helmholtz equation in three dimensions. This is based on the earlier work of the sweeping preconditioner with the moving perfectly matched layers. The key idea is to apply the sweeping preconditioner recursively to the quasi-two-dimensional auxiliary problems introduced in the three-dimensional (3D) sw...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Communications on Pure and Applied Mathematics
سال: 2011
ISSN: 0010-3640
DOI: 10.1002/cpa.20358