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.
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TL;DR: In this paper, a multivariate interpolation scheme for coupling fluid and structural models in 3D space is presented using radial basis functions for numerical aeroelastic computations, a selection of applicable functions is chosen: a classical without compact support, and some recently presented smooth compactly supported radial basis function.
330 citations
TL;DR: In this paper, a front-tracking method is presented to simulate time dependent two-dimensional dendritic solidification of pure substances, based on a finite difference approximation of the heat equation and explicit tracking of the liquid?solid interface.
329 citations
TL;DR: An efficient finite difference model of blood flow through the coronary vessels is developed and applied to a geometric model of the largest six generations of the coronary arterial network by constraining the form of the velocity profile across the vessel radius.
Abstract: An efficient finite difference model of blood flow through the coronary vessels is developed and applied to a geometric model of the largest six generations of the coronary arterial network. By constraining the form of the velocity profile across the vessel radius, the three-dimensional Navier--Stokes equations are reduced to one-dimensional equations governing conservation of mass and momentum. These equations are coupled to a pressure-radius relationship characterizing the elasticity of the vessel wall to describe the transient blood flow through a vessel segment. The two step Lax--Wendroff finite difference method is used to numerically solve these equations. The flow through bifurcations, where three vessel segments join, is governed by the equations of conservation of mass and momentum. The solution to these simultaneous equations is calculated using the multidimensional Newton--Raphson method. Simulations of blood flow through a geometric model of the coronary network are presented demonstrating phy...
329 citations
TL;DR: In this paper, a full vector beam propagation method was used to simulate optical guided waveguide structures by a full-vector beam propagating method and two sets of coupled equations governing the propagation of the transverse electric and magnetic fields were derived systematically.
Abstract: Simulations of optical guided waves in three-dimensional waveguide structures by a full vector beam propagation method are described. Two sets of coupled equations governing the propagation of the transverse electric and magnetic fields are derived systematically. Polarization dependence and coupling due to the vectorial nature of the electromagnetic fields are considered in the formulations. The governing equations are solved subsequently by finite-difference schemes. The vector BPM is first assessed for a step-index circular fiber by comparing the numerical results with the exact analytical solutions. The guided modes of a rib waveguide are then investigated in detail. Comparisons among the scalar, semi-vector and full-vector simulations of the rib waveguide are made. Finally polarization rotation of a periodically loaded rib waveguide operated fully based on the vector nature of the electromagnetic waves is modeled and simulated. >
329 citations
TL;DR: In this article, a general numerical method is presented to compute the electric potential for a macromolecule of arbitrary shape in a solvent with nonzero ionic strength, based on a continuum description of the dielectric and screening properties of the system, which consists of a bounded internal region with discrete charges and an infinite external region.
326 citations