Disk brake squeal noise is mainly due to unstable friction-induced vibration. A typical disk brake system includes two pads, a rotor, a caliper and a piston. In order to predict if a disk brake system will generate squeal, the finite element method (FEM) is used to simulate the system. At the contact interfaces between the pads and the rotor, the normal displacement is continuous and Coulomb’s ...

The minimum residual method, MINRES, is an iterative method for solving a n x n linear system, Ax = b, where is A is a symmetric matrix. It searches for a vector, xk, in the k th Krylov subspace that minimizes the residual, rk = b − Axk. Due to the symmetric nature, the vectors are computed to be the Lanczos vectors, which simplifies to a three-term recurrence, where vk+1 is computed as a linea...

In many large scale scientiic and engineering computations, the solution to a sparse linear system is required. We present a partial unsymmetric nested dissection method that can be used to parallelize any general unsymmetric sparse matrix algorithm whose pivot search can be restricted to a subset of rows and columns in the active submatrix. The submatrix is determined by the partial unsymmetri...

A new unsymmetric matrix, SZu (unsymmetric Szeged matrix) is proposed by analogy to the matrix CJu (unsymmetric Cluj matrix) [1,2]. It is defined and exemplified both for acyclic and cycle-containing structures. Its relation with the CJu matrix is discussed. The derived Szeged numbers are compared to the Wiener matrixand Cluj matrixderived numbers and tested for separating and correlating abili...

A new unsymmetric thioether diamine N - ( 2 - ( 2 - aminophenylthio) ethyl) benzene - 1 , 2 - diamine was prepared through the nucleophilic substitution of cysteaminium chloride with 1 - chloro - 2 - nitrobenzene and then the nitro groups of prepared compuond converted to the amine by zinc powder and ammonium chloride. Then, unsymmetric Schiff bass ligand 2 - ((( 2 - (( 2 - (( 2 - (( 2 - hydrox...

Supernode partitioning for unsymmetric matrices together with complete block diagonal supernode pivoting and asynchronous computation can achieve high gigaflop rates for parallel sparse LU factorization on shared memory parallel computers. The progress in weighted graph matching algorithms helps to extend these concepts further and unsymmetric prepermutation of rows is used to place large matri...

2 Sparse Matrices ……………………………………………………………………………… 4 2.1 The direct solution of sparse unsymmetric linear sets of equations (I.S. Duff and J.K. Reid) …………………………………………………………………………… 4 2.2 The design and use of algorithms for permuting large entries to the diagonal 2.6 Element resequencing for use with a multiple front solver (J. A. Scott) ………… 10 2.7 Exploiting zeros on the diagonal in the direct s...

We present algorithms for the symbolic and numerical factorization phases in the direct solution of sparse unsymmetric systems of linear equations. We have modified a classical symbolic factorization algorithm for unsymmetric matrices to inexpensively compute minimal elimination structures. We give an efficient algorithm to compute a near-minimal data-dependency graph for unsymmetric multifront...

In this paper we investigate a method to improve the performance of sparse LU matrix factorization used to solve unsymmetric linear systems, which appear in many mathematical models. We introduced and used the concept of the supernode for unsymmetric matrices in order to use dense matrix operations to perform the LU factorization for sparse matrices. We describe an algorithm that uses supernode...

Ever since its introduction by Kane Yee over forty years ago, the finitedifference time-domain (FDTD) method has been a widely-used technique for solving the time-dependent Maxwell’s equations that has also inspired many other methods. This paper presents an alternative approach to these equations in the case of spatially-varying electric permittivity and/or magnetic permeability, based on Kryl...