Zichun Yang^1,2,3, Lei Zhang^1,4, Yueyun Cao¹

CMES-Computer Modeling in Engineering & Sciences, Vol.97, No.2, pp. 101-130, 2014, DOI:10.3970/cmes.2014.097.101

Abstract Discretization of inverse problems often leads to systems of linear equations with a highly ill-conditioned coefficient matrix. To find meaningful solutions of such systems, one kind of prevailing and representative approaches is the so-called regularized total least squares (TLS) method when both the system matrix and the observation term are contaminated by some noises. We will survey two such regularization methods in the TLS setting. One is the iterative truncated TLS (TTLS) method which can solve a convergent sequence of projected linear systems generated by Lanczos bidiagonalization. The other one is to convert the Tikhonov… More >

S,erson L. Gonzaga de Oliveira¹, Jéssica Renata Nogueira¹, João Manuel R. S. Tavares²

CMES-Computer Modeling in Engineering & Sciences, Vol.100, No.1, pp. 31-57, 2014, DOI:10.3970/cmes.2014.100.031

Abstract Triangulations and tetrahedrizations are important geometrical discretization procedures applied to several areas, such as the reconstruction of surfaces and data visualization. Delaunay and Voronoi tessellations are discretization structures of domains with desirable geometrical properties. In this work, a systematic review of algorithms with linear-time behaviour to generate 2D/3D Delaunay and/or Voronoi tessellations is presented. More >

Chein-Shan Liu¹, Su-Ying Zhang², Satya N. Atluri³

CMES-Computer Modeling in Engineering & Sciences, Vol.88, No.1, pp. 29-48, 2012, DOI:10.3970/cmes.2012.088.029

Abstract With a detailed investigation of n linear algebraic equations Bx=b, we find that the scaled residual dynamics for y∈Sⁿ⁻¹ is equipped with four structures: the Jordan dynamics, the rotation group SO(n), a generalized Hamiltonian formulation, as well as a metric bracket system. Therefore, it is the first time that we can compute the steplength used in the iterative method by a novel algorithm based on the Jordan structure. The algorithms preserving the length of y are developed as the structure preserving algorithms (SPAs), which can significantly accelerate the convergence speed and are robust enough against the noise More >

A.E. Martínez-Castro¹, I.H. Faris¹, R. Gallego¹

CMES-Computer Modeling in Engineering & Sciences, Vol.87, No.3, pp. 177-206, 2012, DOI:10.3970/cmes.2012.087.177

Abstract In this paper, the identification of hidden defects inside a three-dimen -sional layer is set as an Identification Inverse Problem. This problem is solved by minimizing a cost functional which is linearized with respect to the volume defects, leading to a procedure that requires only computations at the host domain free of defects. The cost functional is stated as the misfit between experimental and computed displacements and spherical and/or ellipsoidal cavities are the defects to locate. The identification of these cavities is based on the measured displacements at a set of points due to time-harmonic… More >

W.J. Santos¹ , J.A.F. Santiago¹, J.C.F Telles¹

CMES-Computer Modeling in Engineering & Sciences, Vol.87, No.1, pp. 23-40, 2012, DOI:10.3970/cmes.2012.087.023

Abstract The aim of this paper is to present numerical simulations of Cathodic Protection (CP) Systems using a Genetic Algorithm (GA) and the Method of Fundamental Solutions (MFS). MFS is used to obtain the solution of the associated homogeneous equation with the non-homogeneous equation subject to nonlinear boundary conditions defined as polarization curves. The adopted GA minimizes a nonlinear error function, whose design variables are the coefficients of the linear superposition of fundamental solutions and the positions of the source points, located outside the problem domain. In this work, the anodes added to the CP system More >

H.W. Tang¹, Y.T. Yang¹, C.K. Chen¹

CMES-Computer Modeling in Engineering & Sciences, Vol.85, No.3, pp. 193-206, 2012, DOI:10.3970/cmes.2012.085.193

Abstract In this article, a new method combining the Mathematical Programming and the Method of Weighted Residual called MP-MWR is presented. Under the validation of maximum principle, and up on the collocation method, the differential equation can be transferred into a bilateral inequality problem. Applying the genetic algorithms helps to find optimal solutions of upper and lower bounds which satisfy the inequalities. Here, the method is verified by analyzing the deflection of superelliptical clamped plate problem. By using this method, the good approximate solution and its error bounds can be obtained effectively and accurately. More >

S.R. Santos¹, L.C. Matioli², A.T. Beck³

CMES-Computer Modeling in Engineering & Sciences, Vol.83, No.1, pp. 23-56, 2012, DOI:10.3970/cmes.2012.083.023

Abstract Solution of structural reliability problems by the First Order method require optimization algorithms to find the smallest distance between a limit state function and the origin of standard Gaussian space. The Hassofer-Lind-Rackwitz-Fiessler (HLRF) algorithm, developed specifically for this purpose, has been shown to be efficient but not robust, as it fails to converge for a significant number of problems. On the other hand, recent developments in general (augmented Lagrangian) optimization techniques have not been tested in aplication to structural reliability problems. In the present article, three new optimization algorithms for structural reliability analysis are presented.… More >

Marco Dondero¹, Adrián P. Cisilino^1,2, J. Pablo Tomba¹

CMES-Computer Modeling in Engineering & Sciences, Vol.78, No.3&4, pp. 225-246, 2011, DOI:10.3970/cmes.2011.078.225

Abstract This paper introduces a numerical methodology for the design of random micro-heterogeneous materials with functionally graded effective thermal conductivities (ETC). The optimization is carried out using representative volume elements (RVEs), a parallel Genetic Algorithm (GA) as optimization method, and a Fast Multipole Boundary Element Method (FMBEM) for the evaluation of the cost function. The methodology is applied for the design of foam-like microstructures consisting of random distributions of circular insulated holes. The temperature field along a material sample is used as objective function, while the spatial distribution of the holes is the design variable. There More >

G.A. Gravvanis¹, K.M. Giannoutakis²

CMES-Computer Modeling in Engineering & Sciences, Vol.71, No.4, pp. 305-330, 2011, DOI:10.3970/cmes.2011.071.305

Abstract In this paper we present parallel explicit approximate inverse matrix techniques for solving sparse linear systems on shared memory systems, which are derived using the finite element method for biharmonic equations in three space variables. Our approach for solving such equations is by considering the biharmonic equation as a coupled equation approach (pair of Poisson equation), using a FE approximation scheme, yielding an inner-outer iteration method. Additionally, parallel approximate inverse matrix algorithms are introduced for the efficient solution of sparse linear systems, based on an anti-diagonal computational approach that eliminates the data dependencies. Parallel explicit More >

Chein-Shan Liu¹, Satya N. Atluri²

CMES-Computer Modeling in Engineering & Sciences, Vol.71, No.3, pp. 279-304, 2011, DOI:10.3970/cmes.2011.071.279

Abstract For solving a system of nonlinear algebraic equations (NAEs) of the type: F(x)=0, or F_i(x_j) = 0, i,j = 1,...,n, a Newton-like algorithm has several drawbacks such as local convergence, being sensitive to the initial guess of solution, and the time-penalty involved in finding the inversion of the Jacobian matrix ∂F_i/∂x_j. Based-on an invariant manifold defined in the space of (x,t) in terms of the residual-norm of the vector F(x), we can derive a gradient-flow system of nonlinear ordinary differential equations (ODEs) governing the evolution of x with a fictitious time-like variable t as an independent variable. … More >