Fabio Henrique Pereira

A wavelet-based algebraic multigrid preconditioner for sparse linear systems

This work considers the use of discrete wavelet transform (DWT), based in filters, in the construction of the hierarchy of matrices in the algebraic multigrid method (AMG). The two-dimensional DWT is applied to produce an approximation of the matrix in each level of the wavelets multiresolution decomposition process. In this procedure an operator is created, formed only by lowpass filters, that is applied to the rows and columns of the matrix capturing this approximation. This same operator is used as an intergrid transfer in the AMG. Wavelet-based algebraic multigrid method (WAMG) was implemented, with Daubechies wavelets of orders 6, 4 and 2, and used as a preconditioner for the generalized minimal residual method (GMRES). Numerical results are presented comparing this new approach with the standard algebraic multigrid as preconditioner for sparse linear systems.

Determination of frequency dependent characteristics of substation grounding systems by vector finite element analysis

A three-dimensional finite-element tool was developed to compute time-harmonic electromagnetic fields and impedance of substation grounding systems. The formulation employs edge-based finite elements for the magnetic vector potential A and nodal shape functions for the electric scalar potential V. The method has been applied in several configurations presented in the literature. The results are compared with both analytical and experimental data reported by other authors, with overall good agreement

A Wavelet-Based Algebraic Multigrid Preconditioning for Iterative Solvers in Finite-Element Analysis

A new approach for algebraic multigrid, based on wavelets, is presented as an efficient preconditioner for iterative solvers applied to the solution of linear systems issued from finite-element analysis. It can be applied to complex systems in which the coefficient matrix violates the M-matrix property, as those arising from ungauged edge-based AV finite-element formulation. When used as a preconditioner for the biconjugate gradient stabilized method it is shown that the proposed technique is more efficient than incomplete Cholesky preconditioner

A fast algebraic multigrid preconditioned conjugate gradient solver

Abstract This work presents a new approach for selecting the coarse grids allowing a faster algebraic multigrid (AMG) preconditioned conjugate gradient solver. This approach is based on an appropriate choice of the parameter α considering the matrix density during the coarsening process which implies in a significant reduction in the matrix dimension at all AMG levels.

Disease spreading in complex networks: A numerical study with Principal Component Analysis

Abstract Disease spreading models need a population model to organize how individuals are distributed over space and how they are connected. Usually, disease agent (bacteria, virus) passes between individuals through these connections and an epidemic outbreak may occur. Here, complex networks models, like Erdös–Rényi, Small-World, Scale-Free and Barábasi–Albert will be used for modeling a population, since they are used for social networks; and the disease will be modeled by a SIR (Susceptible–Infected–Recovered) model. The objective of this work is, regardless of the network/population model, analyze which topological parameters are more relevant for a disease success or failure. Therefore, the SIR model is simulated in a wide range of each network model and a first analysis is done. By using data from all simulations, an investigation with Principal Component Analysis (PCA) is done in order to find the most relevant topological and disease parameters.

A Surrogate-Based Two-Level Genetic Algorithm Optimization Through Wavelet Transform

Despite the surrogate-based two-level algorithms that have been proposed for accelerating the optimization procedures, it may be still expensive for large problems. Therefore, this paper proposes the exploration of the approximation characteristics of the wavelet functions to define a coarse subspace for this kind of approach with relatively few float point operations. The wavelet transform is used to create the coarse model in a two-level genetic algorithm (GA), which is applied to a set of benchmark test problems. Although the coarse model is simpler and less accurate than the fine model, it behaves similarly to this last one and the original function. Moreover, the approach prevented the convergence to local minima whenever the GA presented such behavior and it is faster than the use of principal components analysis.

An efficient two-level preconditioner based on lifting for FEM-BEM equations

The system resulting from the coupled Finite Element Method and Boundary Element Method formulations inherits all characteristics of both finite element and boundary element equation system, i. e., the system is partially sparse and symmetric and partially full and nonsymmetric. Consequently, to solve the resulting coupled equation system is not a trivial task. This paper proposes a new efficient lifting-based two level preconditioner for the coupled global system. The proposed approach is applied to solve the coupled systems resulting from the electromagnetic scattering problem and its performance is evaluated based on the number of iterations and the computational time. Traditional methods based on incomplete and complete LU decompositions are used for comparison.

A Two-Level Genetic Algorithm for Large Optimization Problems

Many local two-level algorithms have been proposed for accelerating the electromagnetic optimization by stochastic algorithms. These algorithms use a combination of a coarse and a fine model in the optimization procedure. Despite the good results, the global convergence properties represent an important drawback of these approaches. A global two-level algorithm had been proposed to deal with the convergence problems, but the requirement to refine the global surrogate model in each step can demand high computational time. This paper introduces a global two-level genetic algorithm that uses single predefined coarse and fine surrogate models, which are defined as an artificial neural network nonlinear regression of a preliminary set of finite element simulations. The benchmark test problem, Hartmann 6, and the problem dealing with the eight-parameter design of superconducting magnetic energy storage have been analyzed..

A Parallel Wavelet-Based Algebraic Multigrid Black-Box Solver and Preconditioner

This work introduces a new parallel wavelet-based algorithm for algebraic multigrid method (PWAMG) using a variation of the standard parallel implementation of discrete wavelet transforms. This new approach eliminates the grid coarsening process in traditional algebraic multigrid setup phase simplifying its implementation on distributed memory machines. The PWAMG method is used as a parallel black-box solver and as a preconditioner in some linear equations systems resulting from circuit simulations and 3D finite elements electromagnetic problems. The numerical results evaluate the efficiency of the new approach as a standalone solver and as preconditioner for the biconjugate gradient stabilized iterative method.

Solution of Nonlinear Magnetic Field Problems by Krylov-Subspace Methods With

The performance of eta-cycle wavelet-based algebraic multigrid preconditioner of iterative methods is investigated. It is applied to the solution of non-linear system of algebraic equations associated with the Newton-Raphson algorithm. Particular attention has been focused in both V- and W-cycle convergence factors, as well as the CPU time. Numerical results show the efficiency of the proposed techniques when compared with classical preconditioners, such as Incomplete Cholesky and Incomplete LU decomposition.