An Improved Quasi-Static Finite-Difference Scheme for Induced Field Evaluation Based on the Biconjugate Gradient Method

2008 ◽  
Vol 55 (7) ◽  
pp. 1800-1808 ◽  
Author(s):  
Hua Wang ◽  
Feng Liu ◽  
A. Trakic ◽  
S. Crozier
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Gradient Method ◽  
Finite Difference Scheme ◽  
Field Evaluation ◽  
Induced Field ◽  
Biconjugate Gradient Method ◽  
Biconjugate Gradient

Conservative modeling of 3-D electromagnetic fields, Part II: Biconjugate gradient solution and an accelerator

Geophysics ◽  
1996 ◽  
Vol 61 (5) ◽  
pp. 1319-1324 ◽  
Author(s):  
J. Torquil Smith
Keyword(s):  
Finite Difference ◽  
Gradient Method ◽  
Preceding Paper ◽  
Finite Difference Approximation ◽  
Staggered Grid ◽  
Difference Approximation ◽  
Low Frequencies ◽  
Linear System Of Equations ◽  
Biconjugate Gradient Method ◽  
Biconjugate Gradient

The preceding paper derives a staggered‐grid, finite‐difference approximation applicable to electromagnetic induction in the Earth. The staggered‐grid, finite‐difference approximation results in a linear system of equations [Formula: see text]x = b, where [Formula: see text] is symmetric but not Hermitian. This is solved using the biconjugate gradient method, preconditioned with a modified, partial Cholesky decomposition of [Formula: see text]. This method takes advantage of the sparsity of [Formula: see text], and converges much more quickly than methods used previously to solve the 3-D induction problem. When simulating a conductivity model at a number of frequencies, the rate of convergence slows as frequency approaches 0. The convergence rate at low frequencies can be improved by an order of magnitude, by alternating the incomplete Cholesky preconditioned biconjugate gradient method with a procedure designed to make the approximate solutions conserve current.

scholarly journals Comparative analysis of the numerical methods for 3D continuation problem for parabolic equation with data on the part of the boundary

2021 ◽  
Vol 2092 (1) ◽  
pp. 012010
Author(s):  
Aleksei Prikhodko ◽  
Maxim Shishlenin
Keyword(s):  
Inverse Problem ◽  
Comparative Analysis ◽  
Parabolic Equation ◽  
Numerical Methods ◽  
Finite Difference ◽  
Difference Scheme ◽  
Gradient Method ◽  
Finite Difference Scheme ◽  
Three Dimensional ◽  
Continuation Problem

Abstract The problem of continuation of the solution of a three-dimensional parabolic equation with data given on a time-like surface is investigated. Two numerical methods for solving the continuation problem are compared: the finite-difference scheme inversion and the solution of inverse problem by gradient method. The functional gradient formula is obtained. The results of numerical calculations are presented.

scholarly journals The convergence of a numerical method for total variation flow

2021 ◽  
Vol 15 ◽  
pp. 174830262110113
Author(s):  
Qianying Hong ◽  
Ming-jun Lai ◽  
Jingyue Wang
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Numerical Method ◽  
Convergence Analysis ◽  
Total Variation ◽  
Iterative Algorithm ◽  
Finite Difference Scheme ◽  
Gradient Flow ◽  
Time Dependent ◽  
Total Variation Flow

We present a convergence analysis for a finite difference scheme for the time dependent partial different equation called gradient flow associated with the Rudin-Osher-Fetami model. We devise an iterative algorithm to compute the solution of the finite difference scheme and prove the convergence of the iterative algorithm. Finally computational experiments are shown to demonstrate the convergence of the finite difference scheme.

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