An ill-posed Cauchy problem for a 3D elliptic PDE with variable coefficients is considered. A well-posed quasi-boundary-value (QBV) problem is given to approximate it. Some stability error estimates are given. For the numerical implementation, a large sparse system is obtained from the discretizing the QBV problem using finite difference method (FDM). A LeftPreconditioner Generalized Minimum Re...

Many applications based on finite element and finite difference methods include the solution of large sparse linear systems using preconditioned iterative methods. Matrix vector multiplication is one of the key operations that has a significant impact on the performance of any iterative solver. In this paper, recent developments in sparse storage formats on vector machines are reviewed. Then, s...

We analyze the discretization of initial and boundary value problems with a stationary interface in one space dimension for the heat equation, the Schrödinger equation, and the wave equation by finite difference methods. Extending the concept of the elliptic projection, well known from the analysis of Galerkin finite element methods, to our finite difference case, we prove second-order error es...

This paper discusses the numerical simulations of heat transfer problem, particularly during welding materials processing. process highly depends on temperature to determine metallurgical properties, strength, and sureness joint welding; hence it is desirable study its flow. Finite difference method (FDM) used discretize partial differential equations (PDEs) obtain systems linear (SLEs), which ...

In this work, we present a marching-on in degree finite difference method (MOD-FDM) to solve the time domain Helmholtz wave equation. This formulation includes electric and magnetic current densities that are expressed in terms of the incident field for scattering problems for an open region to implement a plane wave excitation. The unknown time domain functional variations for the electric fie...

by, for example, a finite difference method in the computational (μ, χ, φ) space. The above standard dipole coordinates is convenient and certainly appropriate for analytical studies in which the Earth’s dipolar field plays central roles. It also works as a base coordinates for the node and cell generation of the finite element method in the dipole geometry [2, 3]. However, when one tries to us...

This study proposes a new forcing scheme suitable for massively-parallel finite-difference simulations of stationary isotropic turbulence. The proposed forcing scheme, named reduced-communication forcing (RCF), is based on the same idea as the conventional large-scale forcing scheme, but requires much less data communication, leading to a high parallel efficiency. It has been confirmed that the...

This paper describes algorithms for threedimensional dynamic stress and fracture analysis using the material point method (MPM). By allowing dual velocity fields at background grid nodes, the method provides exact numerical implementation of explicit cracks in a predominantly meshless method. Crack contact schemes were included for automatically preventing crack surfaces from interpenetration. ...

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 finiteelement method (FEM), and an analytic model developed by applying an internal approximat...

(2) 8;<1>j(r); i = 1, ... ,N mentioned above. A review of the basis sets used in the quantum chemical calculations is given by Wilson [13]. The new developments are the two dimensional fully numerical finite difference method (FDM) [14] and the finite element method (FEM) [15]. It has been shown in both methods that the accuracy to calculate e.g., the total energy is many orders of magnitude be...