We contribute two parallel strategies to compute the exact and approximate inverse of a dense matrix, based on the so-called inverse Sherman-Morrison algorithm and demonstrate their efficiencies on multicore CPU and GPU-equipped computers. Our methods are shown to be much better than a common matrix inverse method, yielding up to 12 times faster performance. A comparison of the performance of t...

We present a fast direct solver methodology for the Dirichlet biharmonic problem in a rectangle. The solver is applicable in the case of the second order Stephenson scheme [34] as well as in the case of a new fourth order scheme, which is discussed in this paper. It is based on the capacitance matrix method ([10], [8]). The discrete biharmonic operator is decomposed into two components. The fir...

Suppose f = p/q is a quotient of two polynomials and that p has degree rp and q has degree rq . Assume that f(A) and f(A+ uv ) are defined where A ∈ R, u ∈ R, and v ∈ R are given and set r = max{rp, rq}. We show how to compute f(A+uv ) in O(rn2) flops assuming that f(A) is available together with an appropriate factorization of the “denominator matrix” q(A). The central result can be interprete...

We develop a simple and efficient FFT-based fast direct solver for the biharmonic equation on a disk. The biharmonic equation is split into a coupled system of harmonic problems. We first use the truncated Fourier series expansion to derive a set of coupled singular ODEs, then we solve those singular equations by second-order finite difference discretizations. Using a radial grid with shifting ...

This paper presents the performance comparison of meta– heuristics algorithms such as DE (Differential Evolution), PSO (Particle Swarm Optimization) and GA (Genetic Algorithm for the problem of Transmission Power Loss (TPL) minimization using Flexible AC Transmission System (FACTS) devices. In addition to that a novel power flow method is proposed using Broyden – Shamanski method with Sherman –...

A new fourth order box-scheme for the Poisson problem in a square with Dirichlet boundary conditions is introduced, extending the approach in [17]. The design is based on a “hermitian box” approach, combining the approximation of the gradient by the fourth order hermitian derivative, with a conservative discrete formulation on boxes of length 2h. The goal is twofold: first to show that fourth o...

The dynamic properties of joints, or inter-component connections, are a principal source uncertainty when modelling complex built-up structures. In the present paper, we propose an interval-based sensitivity analysis (SA) to establish contribution, influence, structure’s uncertain joint dynamics towards its coupled admittance. We choose interval SA as it overcomes limitations conventional local...

In this paper we propose a simple and effective method to find the inverse of arrowhead matrices which often appear in wide areas of applied science and engineering such as wireless communications systems, molecular physics, oscillators vibrationally coupled with Fermi liquid, and eigenvalue problems. Amodified Sherman–Morrison inversematrix method is proposed for computing the inverse of an ar...