My implementation of the discrete difference approximation, as defined by Equation 1, was completed using Matlab and is included as prob1.m. Note that prob1.m accepts a single input argument kMode which is used to toggle λ = 1/2 or λ = h. Before presenting the results of my program, I will briefly outline the architecture of the source code. On lines 21-55 I select the values of {N, h, k} and d...

We present a solver for the 2D high-frequency Helmholtz equation in heterogeneous acoustic media, with online parallel complexity that scales optimally as O(L ), where N is the number of volume unknowns, and L is the number of processors, as long as L grows at most like a small fractional power of N . The solver decomposes the domain into layers, and uses transmission conditions in boundary int...

A parallel program complex for 3D viscous gas flow simulation is presented. This complex is based on explicit finite difference schemes, which are constructed as an approximation of conservation laws (control volume method) and oriented on use of locally refined grids. Special algorithm and utility for nested grid partitioning was created. The principle of program construction permits to introd...

We present in this paper several extremely efficient and accurate spectral-Galerkin methods for secondand fourth-order equations in polar and cylindrical geometries. These methods are based on appropriate variational formulations which incorporate naturally the pole condition(s). In particular, the computational complexities of the Chebyshev–Galerkin method in a disk and the Chebyshev–Legendre–...

In this paper, we will discuss the numerical solution of the two dimensional Heat Equation. An approximation to the solution function is calculated at discrete spatial mesh points, proceeding in discrete time steps. The starting values are given by an initial value condition. We will first explain how to transform the differential equation into a finite difference equation, respectively a set o...

Graphics Processing Units (GPUs) are high performance co-processors originally intended to improve the use and quality of computer graphics applications. Since researchers and practitioners realized the potential of using GPU for general purposes, their applications have been extended to other fields, out of computer graphics scope. The main objective of this paper is to evaluate the impact of ...

Graphical Processing Units (GPUs) are good data-parallel performance accelerators for solving regular mesh partial differential equations (PDEs) whereby low-latency communications and high compute to communications ratios can yield very high levels of computational efficiency. Finite-difference time-domain methods still play an important role for many PDE applications. Iterative multi-grid and ...

We consider algorithms for solving narrow-banded diagonally dominant linear systems which are suitable for multiprocessors. We describe a direct solver similar to that in [12] for tridiagonal systems, and in [9] for solving a banded system on a linearly connected set of processors. We will also provide and analyze a parallel implementation of the partitioning algorithm and the matrix decomposit...

A new resistance simulator for extraction of the parasitic parameters from VLSI layout is presented. The calculation of resistor network is based on the boundary element method (BEM). The computational results indicate that the BEM has an advantage over the finite difference method (FDM) and the finite element method (FEM). Since only discretized equations on the boundary of solved domain need ...