Solving linear equations with a stabilized GPBiCG method
Any residual polynomial of hybrid Bi-Conjugate Gradient (Bi-CG) methods, as Bi-CG STABilized (Bi-CGSTAB), BiCGstab(@?), Generalized Product-type Bi-CG (GPBiCG), and BiCGxMR2, can be expressed as the product of a Lanczos polynomial and a so-called ...
Galerkin methods for the 'Parabolic Equation' Dirichlet problem in a variable 2-D and 3-D topography
The problem analyzed in this paper is a model for the Narrow Angle parabolic approximation of Helmholtz equation in environments in R^n, n=2,3, of variable topography used in underwater acoustics. By applying a horizontal bottom transformation combined ...
The effect of mesh modification in time on the error control of fully discrete approximations for parabolic equations
We consider fully discrete schemes for linear parabolic problems discretized by the Crank-Nicolson method in time and the standard finite element method in space. We study the effect of mesh modification on the stability of fully discrete approximations ...
Active and passive symmetrization of Runge-Kutta Gauss methods
A symmetrizer for a symmetric Runge-Kutta method is designed to preserve the asymptotic error expansion in even powers of the stepsize and to provide damping for stiff initial value problems. In this paper we study symmetrizers for the Gauss methods ...
An efficient parallel iteration method for multiscale analysis of chemical vapor deposition processes
A fixed point type iteration method is applied for coupling multiple length scales in Chemical Vapor Deposition (CVD) processes. A Reactor Scale Model (RSM), used for the description of the macro-scale in the bulk phase of a CVD reactor, is coupled with ...
Reduced averaging of directional derivatives in the vertices of unstructured triangulations
Assume that T"h is a conforming regular triangulation without obtuse angles of a bounded polygonal domain @W@?@?^2. For an arbitrary unit vector z and an inner or so-called semi-inner vertex a, the method of reduced averaging for the approximation of ...
Numerical solution of discontinuous differential systems: Approaching the discontinuity surface from one side
We consider the numerical integration of discontinuous differential systems of ODEs of the type: x^'=f"1(x) when h(x)<0 and x^'=f"2(x) when h(x)>0, and with f"1<>f"2 for x@__ __@S, where @S:={x:h(x)=0} is a smooth co-dimension one discontinuity surface. ...
Application of a finite difference computational model to the simulation of earthquake generated tsunamis
Tsunamis are long waves and commonly modeled with the shallow-water wave approximation of the equations of motion. The calculation of tsunami inundation remains after two decades of progress a vexing and temperamental computation exquisitely dependent ...
An approximation method for solving systems of Volterra integro-differential equations
The approximate method for solving a system of nonlinear Volterra integro-differential equations introduced in this paper, involves the use of biorthogonal systems in adequate spaces of continuous functions associated with such a system. That allows to ...
Local radial basis function collocation method along with explicit time stepping for hyperbolic partial differential equations
This paper tackles an improved Localized Radial Basis Functions Collocation Method (LRBFCM) for the numerical solution of hyperbolic partial differential equations (PDEs). The LRBFCM is based on multiquadric (MQ) Radial Basis Functions (RBFs) and ...
A finite element discretization of the standard parabolic equation in generalized boundary fitting coordinates
A simplified, but quantitatively reliable approximation of atmospheric sound propagation is given by the standard parabolic equation. The waveguide is a cylindrically symmetric, unbounded, domain with an irregular lower boundary. The associated initial-...
A well-balanced shock-capturing hybrid finite volume-finite difference numerical scheme for extended 1D Boussinesq models
A formally fourth-order well-balanced hybrid finite volume/difference (FV/FD) numerical scheme for approximating the conservative form of two 1D extended Boussinesq systems is presented. The FV scheme is of the Godunov type and utilizes Roe@?s ...
A Nitsche type method for stress fields calculation in dissimilar material with interface crack
This work deals with the crack problem simulation in dissimilar media. It proposes a new numerical method derived from a Nitsche approach for handling interface conditions in the elasticity equations. The Nitsche method, introduced to impose weakly ...
A globally adaptive explicit numerical method for exploding systems of ordinary differential equations
This paper considers the mathematical framework of a sliced-time computation method for explosive solutions to systems of ordinary differential equations: Y(t)@__ __R^k:dYdt=F(Y), 0 =1} determined by an end-of-slice condition that controls the growth of ...
Iterative refinement techniques for solving block linear systems of equations
We study the numerical properties of classical iterative refinement (IR) and k-fold iterative refinement (RIR) for computing the solution of a nonsingular linear system of equations Ax=b with A partitioned into blocks using floating point arithmetic. We ...
Rate of convergence of higher order methods
Methods like the Chebyshev and the Halley method are well known methods for solving nonlinear systems of equations. They are members in the Halley class of methods and all members in this class have local and third order rate of convergence. They are ...
Finite element approximations for a linear fourth-order parabolic SPDE in two and three space dimensions with additive space-time white noise
We consider an initial and Dirichlet boundary value problem for a linear fourth-order stochastic parabolic equation, in two or three space dimensions, forced by an additive space-time white noise. Discretizing the space-time white noise a modeling error ...