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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01 May 1977
TL;DR: A comprehensive and illustrated account of the use of finite difference computational methods for heat transfer calculations is presented in this paper, which is oriented towards the practical man who needs a complete work to enable him to understand and apply the methods to solve his problems.
Abstract: A comprehensive and illustrated account of the use of finite difference computational methods for heat transfer calculations is presented. The methods are basically simple but offer a powerful tool to the engineering designer or researcher faced with heat transfer problems of a difficult, or more often impossible, analytical nature. The text is oriented towards the practical man who needs a complete work to enable him to understand and apply the methods to solve his problems. Information is provided about all the many facets of analyzing and solving conductive heat transfer problems, including the computer programming aspects. The general problem considered is that of calculating the distribution of temperature or temperature history in a physical system in which heat transfer is taking place. A special attribute offered is the strong practical emphasis, and recent ideas on numerical solution techniques, and their implementation via Fortran computer programs. The various numerical solution schemes are illustrated through a series of worked examples, tabular computations, Fortran programs and case studies.
186 citations
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TL;DR: New finite difference methods using Cartesian grids are developed for elliptic interface problems with variable discontinuous coefficients, singular sources, and nonsmooth or even discontinuous solutions to satisfy the sign property of the discrete maximum principle using quadratic optimization techniques.
Abstract: New finite difference methods using Cartesian grids are developed for elliptic interface problems with variable discontinuous coefficients, singular sources, and nonsmooth or even discontinuous solutions. The new finite difference schemes are constructed to satisfy the sign property of the discrete maximum principle using quadratic optimization techniques. The methods are shown to converge under certain conditions using comparison functions. The coefficient matrix of the resulting linear system of equations is an M-matrix and is coupled with a multigrid solver. Numerical examples are also provided to show the efficiency of the proposed methods.
186 citations
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TL;DR: In this article, a new concept of field computation is presented based on the postulate of the existence of linear equations of the discretized nodal values of the fields, different from the conventional equations, but leading to the same solutions.
Abstract: Numerical computations of frequency domain field problems or elliptical partial differential equations may be based on differential equations or integral equations. The new concept of field computation presented in this paper is based on the postulate of the existence of linear equations of the discretized nodal values of the fields, different from the conventional equations, but leading to the same solutions. The postulated equations are local and invariant to excitation. It is shown how the equations can be determined by a sequence of "measures". The measured equations are particularly useful at the mesh boundary, where the finite difference methods fail. The measured equations do not assume the physical condition of absorption, so they are also applicable to concave boundaries. Using the measured equations, one can terminate the finite difference mesh very close to the physical boundary and still obtain robust solutions. It will definitely make a great impact on the way one applies finite difference and finite element methods in many problems. Computational results using the measured equations of invariance in two and three dimensions are presented. >
185 citations
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TL;DR: In this article, a two-dimensional airfoil with either a bilinear or cubic structural nonlinearity in pitch, and subject to incompressible flow has been analyzed using Wagner's function.
184 citations
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TL;DR: A general approach for connecting covolume or finite volume element methods for variable coefficient elliptic and parabolic problems on convex smooth domains in the plane is introduced and the maximur norm error in the gradient is shown to be of first order.
Abstract: In this paper we consider covolume or finite volume element methods for variable coefficient elliptic and parabolic problems on convex smooth domains in the plane. We introduce a general approach for connecting these methods with finite element method analysis. This unified approach is used to prove known convergence results in the H 1 , L 2 norms and new results in the max-norm. For the elliptic problems we demonstrate that the error u-u h between the exact solution u and the approximate solution u h in the maximum norm is O(h 2 |ln h|) in the linear element case. Furthermore, the maximur norm error in the gradient is shown to be of first order. Similar results hold for the parabolic problems.
184 citations