Multi-color Difference Schemes of Helmholtz Equation and Its Parallel Fast Solver over 3-D Dodecahedron Partitions

2005 ◽  
pp. 301-308
Author(s):  
Jiachang Sun
Keyword(s):  
Helmholtz Equation ◽  
Color Difference ◽  
Difference Schemes ◽  
Fast Solver

A fast solver for the Helmholtz equation on long, thin structures

2005 ◽  
Vol 53 (9) ◽  
pp. 2911-2919
Author(s):  
Hongwei Cheng ◽  
Junsheng Zhao ◽  
V. Rokhlin ◽  
N. Yarvin
Keyword(s):  
Helmholtz Equation ◽  
Thin Structures ◽  
Fast Solver

scholarly journals SIXTH-ORDER ACCURATE FINITE DIFFERENCE SCHEMES FOR THE HELMHOLTZ EQUATION

2006 ◽  
Vol 14 (03) ◽  
pp. 339-351 ◽  
Author(s):  
I. SINGER ◽  
E. TURKEL
Keyword(s):  
Finite Difference ◽  
Helmholtz Equation ◽  
Truncation Error ◽  
Model Problem ◽  
Difference Schemes ◽  
Sixth Order ◽  
Finite Difference Schemes ◽  
Local Truncation Error ◽  
Two Dimensional ◽  
Truncation Order

We develop and analyze finite difference schemes for the two-dimensional Helmholtz equation. The schemes which are based on nine-point approximation have a sixth-order accurate local truncation order. The schemes are compared with the standard five-point pointwise representation, which has second-order accurate local truncation error and a nine-point fourth-order local truncation error scheme based on a Padé approximation. Numerical results are presented for a model problem.

scholarly journals A Fast Solver for the Fractional Helmholtz Equation

2021 ◽  
Vol 43 (2) ◽  
pp. A1362-A1388
Author(s):  
Christian Glusa ◽  
Harbir Antil ◽  
Marta D'Elia ◽  
Bart van Bloemen Waanders ◽  
Chester J. Weiss
Keyword(s):  
Helmholtz Equation ◽  
Fast Solver

scholarly journals Modified Finite Difference Schemes on Uniform Grids for Simulations of the Helmholtz Equation at Any Wave Number

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Hafiz Abdul Wajid ◽  
Naseer Ahmed ◽  
Hifza Iqbal ◽  
Muhammad Sarmad Arshad
Keyword(s):  
Finite Difference ◽  
Helmholtz Equation ◽  
Bloch Wave ◽  
Difference Schemes ◽  
Wave Number ◽  
Uniform Grid ◽  
Finite Difference Schemes ◽  
Radiation Boundary Conditions ◽  
Fine Mesh ◽  
Uniform Grids

We construct modified forward, backward, and central finite difference schemes, specifically for the Helmholtz equation, by using the Bloch wave property. All of these modified finite difference approximations provide exact solutions at the nodes of the uniform grid for the second derivative present in the Helmholtz equation and the first derivative in the radiation boundary conditions for wave propagation. The most important feature of the modified schemes is that they work for large as well as low wave numbers, without the common requirement of a very fine mesh size. The superiority of the modified finite difference schemes is illustrated with the help of numerical examples by making a comparison with standard finite difference schemes.

scholarly journals A Fast Solver for the Fractional Helmholtz Equation.

2019 ◽  
Author(s):  
Christian Alexander Glusa ◽  
Marta D'Elia ◽  
Harbir Antil ◽  
Chester Joseph Weiss ◽  
Bart G. van Bloemen Waanders
Keyword(s):  
Helmholtz Equation ◽  
Fast Solver
Sign in / Sign up

Export Citation Format

Share Document