Block-diagonalization of sparse equivariant discretization matrices is studied. Such matrices typically arise when partial differential equations that evolve in symmetric geometries are discretized via the finite element method or via finite differences. By considering sparse equivariant matrices as equivariant graphs, we identify a condition for when block-diagonalization via a sparse variant ...

This paper describes an iterative aggregation/disaggregation method for computing the stationary probability vector of a nearly completely decomposable Markov chain. The emphasis is on the implementation of the algorithm and on the results that are obtained when it is applied to three modelling examples that have been used in the analysis of computer/communication systems. Where applicable, a c...

We describe an efficient parallel solution for the problem of finding the shortest Euclidean path between two points in three dimensional space in the presence of polyhedral obstacles. We consider the important case where the order in which the obstacles are encountered in this shortest path is known. In particular for this case we describe an efficient parallel numerical iterative method on a ...

In this work we devise eecient algorithms for nding the search directions for interior point methods applied to linear programming problems. There are two innovations. The rst is the use of updating of preconditioners computed for previous barrier parameters. The second is an adaptive automated procedure for determining whether to use a direct or iterative solver, whether to reinitialize or upd...

Abstract. Symmetry and antisymmetry properties of a class of elliptic partial di erential equations are exploited to prove when a particular parallel multilevel algorithm is a direct method rather than the usual iterative method. No smoothing is required for this result. Examples are presented, including variable coe cient ones. A connection between the algorithm in this article and domain deco...

Structural joints provide connection between structural element (beam, plate etc.) in order to construct a whole assembled structure. There are many types of structural joints such as bolted joint, riveted joints and welded joints. The joints structures significantly contribute to structural stiffness and dynamic behaviour of structures hence the main objectives of this paper are to review on m...

A main problem in adaptive optics is to reconstruct the phase spectrum given noisy phase differences. We present an efficient approach to solve the least-squares minimization problem resulting from this reconstruction, using either a truncated singular value decomposition (TSVD)-type or a Tikhonov-type regularization. Both of these approaches make use of Kronecker products and the generalized s...

A new method for the dynamic analysis of the vertical vehicle-structure interaction is presented. The vehicle and structure systems can be discretized with various types of finite elements and may have any degree of complexity. The equations of both systems are complemented with additional compatibility equations to ensure contact between the vehicles and the structure. The equations of motion ...

In this paper we describe a method for computing matrix CR bounds for image reconstruction problems using an iterative algorithm that avoids the intractable inversion of the Fisher matrix required by direct methods. The algorithm produces a close approximation to the CR bound requiring only o(n2) floating point operations per pixel of interest; an order of magnitude saving relative to the O(n3)...

Discrete body of revolution (DBOR) codes can accelerate moment method (MoM) solutions for scattering geometries possessing discrete circular symmetry. Traditional DBOR formulations require modifications to the incident field, such as decomposition into circular modes. While appropriate for methods employing direct solvers, approaches employing iterative solvers are disadvantaged by this dramati...