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, it is shown that the time-dependent sensitivity can be derived directly from the adjoint model solution, that is, the sensitivity to initial conditions as function of the initial time.
Abstract: Adjoint models are used for atmospheric and oceanic sensitivity studies in order to efficiently evaluate the sensitivity of a cost function (e.g., the temperature or pressure at some target time tf, averaged over some region of interest) with respect to the three-dimensional model initial conditions. The time-dependent sensitivity, that is the sensitivity to initial conditions as function of the initial time ti, may be obtained directly and most efficiently from the adjoint model solution. There are two approaches to formulating an adjoint of a given model. In the first (“finite difference of adjoint”), one derives the continuous adjoint equations from the linearized continuous forward model equations and then formulates the finite-difference implementation of the continuous adjoint equations. In the second (“adjoint of finite difference”), one derives the finite-difference adjoint equations directly from the finite difference of the forward model. It is shown here that the time-dependent sensiti...
117 citations
17 May 1998
TL;DR: In this article, the effect of the boundary condition representation and the introduced errors on temperature response at the heat source is studied, particularly for large surges of a short time duration, and an analytic model developed by applying an internal approximation of the heat diffusion problem is developed.
Abstract: The literature proposes some thermal models needed for the electrothermal simulation of power electronic systems. This paper gives a useful analysis about the choice of the thermal model circuit networks, equivalent to a discretization of the heat equation by the finite difference method (FDM) and the finite-element method (FEM), and an analytic model developed by applying an internal approximation of the heat diffusion problem. The effect of the boundary condition representation and the introduced errors on temperature response at the heat source are studied. This study is advantageous, particularly for large surges of a short time duration.
117 citations
TL;DR: In this article, a finite-difference time-domain (FDTD) solution of the electromagnetic wave propagation in the radar frequency band is presented. But the FDTD algorithm does not account for the frequency dependence of the dielectric permittivity and electrical conductivity typical of many near surface materials.
Abstract: Realistic modeling of electromagnetic wave propagation in the radar frequency band requires a full solution of Maxwell’s equations as well as an adequate description of the material properties. We present a finite‐difference time‐domain (FDTD) solution of Maxwell’s equations that allows accounting for the frequency dependence of the dielectric permittivity and electrical conductivity typical of many near‐surface materials. This algorithm is second‐order accurate in time and fourth‐order accurate in space, conditionally stable, and computationally only marginally more expensive than its standard equivalent without frequency‐dependent material properties. Empirical rules on spatial wavefield sampling are derived through systematic investigations of the influence of various parameter combinations on the numerical dispersion curves. Since this algorithm intrinsically models energy absorption, efficient absorbing boundaries are implemented by surrounding the computational domain by a thin (⩽2 dominant waveleng...
117 citations
TL;DR: The boundary integral equation method (BIEM) for porous elasticity is proposed in this article, where the fundamental kernels for the integral equations are solved in closed forms for the case of isotropic material.
Abstract: For physical phenomena governed by the Biot model of porous-elasticity, a reciprocal relation, similar to the Betti's recoprocal theorem in elasticity, is constructed in Laplace transformed space. Integrating the reciprocal relation enables one to formulate boundary integral equations. The fundamental kernels for the integral equations are solved in closed forms for the case of isotropic material. Numerical implementation of two-dimensional problems includes finite element ideas of discretization and polynomial interpolation, and numerical inversion of a Laplace transform. Practical applications of the method are found in consolidation problems in soils which contain compressible as well as incompressible pore fluids. Also, as a numerical experiment, consolidation of partially saturated soil is simulated and interesting phenomena are observed. The currently developed boundary integral equation method (BIEM) for porous-elasticity may be viewed as an efficient and accurate alternative of existing finite element and finite difference methods. For linear consolidation problems, application of BIEM is always preferred to the other numerical methods whenever possible.
117 citations
TL;DR: In this paper, a numerical method for determining the flame speed and the structure of freely propagating, adiabatic flames is discussed. But the method is computationally faster than other methods, and it is potentially more accurate because it employs an adaptive gridding strategy.
Abstract: Abstract–We discuss a numerical method for determining the flame speed and the structure of freely propagating, adiabatic flames. The method uses a finite difference procedure in which the nonlinear difference equations are solved by a damped, modified, Newton method. This approach is in contrast to the traditional approach of solving a related transient problem until a steady-state solution i5 achieved. Our method is computationally faster than other methods, and it is potentially more accurate because it employs an adaptive gridding strategy. We demonstrate its use for the determination of hydrogen-air flame speeds.
117 citations