Topic
Finite difference method
About: Finite difference method is a research topic. Over the lifetime, 21603 publications have been published within this topic receiving 468852 citations. The topic is also known as: Finite-difference methods & FDM.
Papers published on a yearly basis
Papers
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TL;DR: It is proved that the filter can control the total variation of the solution and also produce sharp discrete shocks in a nonlinear conservation form filter.
Abstract: A new type of methods for the numerical approximation of hyperbolic conservation laws with discontinuous solution is introduced. The methods are based on standard finite difference schemes. The difference solution is processed with a nonlinear conservation form filter at every time level to eliminate spurious oscillations near shocks. It is proved that the filter can control the total variation of the solution and also produce sharp discrete shocks. The method is simpler and faster than many other high resolution schemes for shock calculations. Numerical examples in one and two space dimensions are presented.
97 citations
TL;DR: In this article, it is shown that it is possible to transform the original physical problem to one that has propagation velocities with less frequency dependence, and the number of time steps necessary for a signal to travel a certain distance with the lowest velocity is significantly reduced.
Abstract: In the low-frequency limit, the displacement currents in the Maxwell equations can be neglected. However, for numerical simulations, a small displacement current should be present to achieve numerical stability. This requirement leads to a large range of propagation velocities with high velocities for the high frequencies and low velocities for the low frequencies. As a consequence, the number of time steps may become large. I show that it is possible to transform mathematically the original physical problem to one that has propagation velocities with less frequency dependence. Hence, the number of time steps necessary for a signal to travel a certain distance with the lowest velocity is significantly reduced. A typical example shows a reduction in computational time by a factor of 40. A comparison of the solutions from plane-layered modeling in the frequency and wavenumber domain and the proposed method shows good agreement between the two. The proposed method can also be used for other systems of diffusive equations.
97 citations
TL;DR: In this article, the authors studied laminar, steady state flow in helically coiled tubes at a constant wall temperature, numerically and experimentally, using a finite difference method with projection algorithm using FORTRAN programming language.
97 citations
TL;DR: The generalized Vandermonde determinant is introduced, and general explicit finite difference formulas with arbitrary order accuracy for approximating first and higher derivatives, which are applicable to unequally or equally spaced data are presented.
97 citations
TL;DR: In this paper, an algorithm to invert geophysical magnetic data to recover 3D distributions of subsurface magnetic susceptibility when the bodies have complicated geometry and possibly high magnetic susceptibility was developed.
Abstract: SUMMARY
We develop an algorithm to invert geophysical magnetic data to recover 3-D distributions of subsurface magnetic susceptibility when the bodies have complicated geometry and possibly high magnetic susceptibility. For the associated forward modelling problem, a full solution to Maxwell's equations for source-free magnetostatics is developed in the differential equation domain using a finite volume discretization. The earth region of interest is discretized into many prismatic cells, each with constant susceptibility. The resulting system of discrete equations is solved using an ILU-preconditioned Bi-Conjugate Gradient Stabilized (BiCGStab) algorithm. Formulations for total and secondary field computations are developed and tested against analytic solutions and against a solution in the integral equation domain. The finite volume forward modelling method forms the foundation for a subsequent inversion algorithm. The underdetermined inverse problem is solved as an unconstrained optimization problem and an objective function composed of data misfit and a regularization term is minimized using a Gauss–Newton search. At each iteration, the CGLS algorithm is used to solve for the search direction. The inversion code is tested on synthetic data from both geometrically simple and complicated bodies and on field survey data collected over a planted ferrous shipping container.
97 citations