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Coefficient Matrix (coefficient + matrix)

Distribution by Scientific Domains

Engineering	76%
Mathematics and Statistics	23%

Selected Abstracts

System identification applied to long-span cable-supported bridges using seismic records

EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 3 2008
Dionysius M. Siringoringo
Abstract This paper presents the application of system identification (SI) to long-span cable-supported bridges using seismic records. The SI method is based on the System Realization using Information Matrix (SRIM) that utilizes correlations between base motions and bridge accelerations to identify coefficient matrices of a state-space model. Numerical simulations using a benchmark cable-stayed bridge demonstrate the advantages of this method in dealing with multiple-input multiple-output (MIMO) data from relatively short seismic records. Important issues related to the effects of sensor arrangement, measurement noise, input inclusion, and the types of input with respect to identification results are also investigated. The method is applied to identify modal parameters of the Yokohama Bay Bridge, Rainbow Bridge, and Tsurumi Fairway Bridge using the records from the 2004 Chuetsu-Niigata earthquake. Comparison of modal parameters with the results of ambient vibration tests, forced vibration tests, and analytical models are presented together with discussions regarding the effects of earthquake excitation amplitude on global and local structural modes. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Diagonalization procedure for scaled boundary finite element method in modeling semi-infinite reservoir with uniform cross-section

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2009
S. M. Li
Abstract To improve the ability of the scaled boundary finite element method (SBFEM) in the dynamic analysis of dam,reservoir interaction problems in the time domain, a diagonalization procedure was proposed, in which the SBFEM was used to model the reservoir with uniform cross-section. First, SBFEM formulations in the full matrix form in the frequency and time domains were outlined to describe the semi-infinite reservoir. No sediments and the reservoir bottom absorption were considered. Second, a generalized eigenproblem consisting of coefficient matrices of the SBFEM was constructed and analyzed to obtain corresponding eigenvalues and eigenvectors. Finally, using these eigenvalues and eigenvectors to normalize the SBFEM formulations yielded diagonal SBFEM formulations. A diagonal dynamic stiffness matrix and a diagonal dynamic mass matrix were derived. An efficient method was presented to evaluate them. In this method, no Riccati equation and Lyapunov equations needed solving and no Schur decomposition was required, which resulted in great computational costs saving. The correctness and efficiency of the diagonalization procedure were verified by numerical examples in the frequency and time domains, but the diagonalization procedure is only applicable for the SBFEM formulation whose scaling center is located at infinity. Copyright © 2009 John Wiley & Sons, Ltd. [source]

A continued-fraction-based high-order transmitting boundary for wave propagation in unbounded domains of arbitrary geometry

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2008
Mohammad Hossein Bazyar
Abstract A high-order local transmitting boundary is developed to model the propagation of elastic waves in unbounded domains. This transmitting boundary is applicable to scalar and vector waves, to unbounded domains of arbitrary geometry and to anisotropic materials. The formulation is based on a continued-fraction solution of the dynamic-stiffness matrix of an unbounded domain. The coefficient matrices of the continued fraction are determined recursively from the scaled boundary finite element equation in dynamic stiffness. The solution converges rapidly over the whole frequency range as the order of the continued fraction increases. Using the continued-fraction solution and introducing auxiliary variables, a high-order local transmitting boundary is formulated as an equation of motion with symmetric and frequency-independent coefficient matrices. It can be coupled seamlessly with finite elements. Standard procedures in structural dynamics are directly applicable for evaluating the response in the frequency and time domains. Analytical and numerical examples demonstrate the high rate of convergence and efficiency of this high-order local transmitting boundary. Copyright © 2007 John Wiley & Sons, Ltd. [source]

On the inverse of generalized ,-matrices with singular leading term

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2006
N. A. Dumont
Abstract An algorithm is introduced for the inverse of a ,-matrix given as the truncated series A0,i,A1,,2A2+i,3A3+,4A4+···+O(,n+1) with square coefficient matrices and singular leading term A0. Moreover, A1 may be conditionally singular and no restrictions are made for the remaining terms. The result is a ,-matrix given as a unique, truncated series of the same error order. Motivation for this problem is the evaluation of the frequency-dependent stiffness matrix of general boundary or macro-finite elements in the frame of a hybrid variational formulation that is based on a flexibility matrix F expressed as a truncated power series of the circular frequency ,. Copyright © 2005 John Wiley & Sons, Ltd. [source]

An accurate gradient and Hessian reconstruction method for cell-centered finite volume discretizations on general unstructured grids

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 9 2010
Lee J. Betchen
Abstract In this paper, a novel reconstruction of the gradient and Hessian tensors on an arbitrary unstructured grid, developed for implementation in a cell-centered finite volume framework, is presented. The reconstruction, based on the application of Gauss' theorem, provides a fully second-order accurate estimate of the gradient, along with a first-order estimate of the Hessian tensor. The reconstruction is implemented through the construction of coefficient matrices for the gradient components and independent components of the Hessian tensor, resulting in a linear system for the gradient and Hessian fields, which may be solved to an arbitrary precision by employing one of the many methods available for the efficient inversion of large sparse matrices. Numerical experiments are conducted to demonstrate the accuracy, robustness, and computational efficiency of the reconstruction by comparison with other common methods. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Strong stability radii of positive linear time-delay systems

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 10 2005
Pham Huu Anh NgocArticle first published online: 18 MAY 200
Abstract In this paper, we study robustness of the strong delay-independent stability of linear time-delay systems under multi-perturbation and affine perturbation of coefficient matrices via the concept of strong delay - independent stability radius (shortly, strong stability radius). We prove that for class of positive time-delay systems, complex and real strong stability radii of positive linear time-delay systems under multi-perturbations (or affine perturbations) coincide and they are computed via simple formulae. Apart from that, we derive solution of a global optimization problem associated with the problem of computing of the strong stability radii of a positive linear time-delay system. An example is given to illustrate the obtained results. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Robust ,, filtering for uncertain Markovian jump linear systems,

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 5 2002
Carlos E. de Souza
Abstract This paper investigates the problem of ,, filtering for a class of uncertain Markovian jump linear systems. The uncertainty is assumed to be norm-bounded and appears in all the matrices of the system state-space model, including the coefficient matrices of the noise signals. It is also assumed that the jumping parameter is available. We develop a methodology for designing a Markovian jump linear filter that ensures a prescribed bound on the ,2 -induced gain from the noise signals to the estimation error, irrespective of the uncertainty. The proposed design is given in terms of linear matrix inequalities. Copyright © 2002 John Wiley & Sons, Ltd. [source]

Two-grid methods for banded linear systems from DCT III algebra

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 2-3 2005
R. H. Chan
Abstract We describe a two-grid and a multigrid method for linear systems whose coefficient matrices are point or block matrices from the cosine algebra generated by a polynomial. We show that the convergence rate of the two-grid method is constant independent of the size of the given matrix. Numerical examples from differential and integral equations are given to illustrate the convergence of both the two-grid and the multigrid method. Copyright © 2004 John Wiley & Sons, Ltd. [source]

Partial pole assignment for the vibrating system with aerodynamic effect

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 1 2004
Wen-Wei Lin
Abstract The partial pole assignment (PPA) problem is the one of reassigning a few unwanted eigenvalues of a control system by feedback to suitably chosen ones, while keeping the remaining large number of eigenvalues unchanged. The problem naturally arises in modifying dynamical behaviour of the system. The PPA has been considered by several authors in the past for standard state,space systems and for quadratic matrix polynomials associated with second-order systems. In this paper, we consider the PPA for a cubic matrix polynomial arising from modelling of a vibrating system with aerodynamics effects and derive explicit formulas for feedback matrices in terms of the coefficient matrices of the polynomial. Our results generalize those of a quadratic matrix polynomial by Datta et al. (Linear Algebra Appl. 1997;257: 29) and is based on some new orthogonality relations for eigenvectors of the cubic matrix polynomial, which also generalize the similar ones reported in Datta et al. (Linear Algebra Appl. 1997;257: 29) for the symmetric definite quadratic pencil. Besides playing an important role in our solution for the PPA, these orthogonality relations are of independent interests, and believed to be an important contribution to linear algebra in its own right. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Analysis of algebraic systems arising from fourth-order compact discretizations of convection-diffusion equations

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 2 2002
Ashvin Gopaul
Abstract We study the properties of coefficient matrices arising from high-order compact discretizations of convection-diffusion problems. Asymptotic convergence factors of the convex hull of the spectrum and the field of values of the coefficient matrix for a one-dimensional problem are derived, and the convergence factor of the convex hull of the spectrum is shown to be inadequate for predicting the convergence rate of GMRES. For a two-dimensional constant-coefficient problem, we derive the eigenvalues of the nine-point matrix, and we show that the matrix is positive definite for all values of the cell-Reynolds number. Using a recent technique for deriving analytic expressions for discrete solutions produced by the fourth-order scheme, we show by analyzing the terms in the discrete solutions that they are oscillation-free for all values of the cell Reynolds number. Our theoretical results support observations made through numerical experiments by other researchers on the non-oscillatory nature of the discrete solution produced by fourth-order compact approximations to the convection-diffusion equation. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 155,178, 2002; DOI 10.1002/num.1041 [source]

Robust decentralized H, control for interconnected descriptor systems with norm-bounded uncertainties,,

ASIAN JOURNAL OF CONTROL, Issue 1 2009
Ning Chen
Abstract This paper considers a robust decentralized H, control problem for interconnected descriptor systems. The uncertainties are assumed to be time-invariant, norm-bounded, and existing in both the system and control input matrices. Our interest is focused on dynamic output feedback. A sufficient condition for an uncertain interconnected descriptor system to be robustly stabilizable H, control with a specified disturbance attenuation level is derived in terms of a nonlinear matrix inequality (NMI). A two-stage homotopy method is employed to solve the NMI iteratively. First, a decentralized controller for the nominal descriptor system is computed by imposing block-diagonal constraints on the coefficient matrices of the controller gradually. Then, the decentralized controller is gradually modified from the nominal descriptor system (without uncertainties) to the original system with uncertainties. On each stage, groups of variables are fixed alternately at the iterations to reduce the NMI to linear matrix inequalities (LMIs). An example is given to show the usefulness of this method. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source]

Regularizability Of Linear Descriptor Systems Via Output Plus Partial State Derivative Feedback

ASIAN JOURNAL OF CONTROL, Issue 3 2003
Guang-Ren Duan
ABSTRACT Regularizability of a linear descriptor system via output plus partial state derivative feedback is studied. Necessary and sufficient conditions are obtained, which are only dependent upon the open-loop coefficient matrices. It is also shown that under these necessary and sufficient conditions, "almost all" output plus partial state derivative feedback controllers can regularize a regularizable linear descriptor system. The proposed conditions generalize many existing results. The presented example demonstrates the proposed results. [source]

Fast multipole boundary element analysis of two-dimensional elastoplastic problems

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 10 2007
P. B. Wang
Abstract This paper presents a fast multipole boundary element method (BEM) for the analysis of two-dimensional elastoplastic problems. An incremental iterative technique based on the initial strain approach is employed to solve the nonlinear equations, and the fast multipole method (FMM) is introduced to achieve higher run-time and memory storage efficiency. Both of the boundary integrals and domain integrals are calculated by recursive operations on a quad-tree structure without explicitly forming the coefficient matrix. Combining multipole expansions with local expansions, computational complexity and memory requirement of the matrix,vector multiplication are both reduced to O(N), where N is the number of degrees of freedom (DOFs). The accuracy and efficiency of the proposed scheme are demonstrated by several numerical examples. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Reduced-order modeling of parameterized PDEs using time,space-parameter principal component analysis,

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2009
C. Audouze
Abstract This paper presents a methodology for constructing low-order surrogate models of finite element/finite volume discrete solutions of parameterized steady-state partial differential equations. The construction of proper orthogonal decomposition modes in both physical space and parameter space allows us to represent high-dimensional discrete solutions using only a few coefficients. An incremental greedy approach is developed for efficiently tackling problems with high-dimensional parameter spaces. For numerical experiments and validation, several non-linear steady-state convection,diffusion,reaction problems are considered: first in one spatial dimension with two parameters, and then in two spatial dimensions with two and five parameters. In the two-dimensional spatial case with two parameters, it is shown that a 7 × 7 coefficient matrix is sufficient to accurately reproduce the expected solution, while in the five parameters problem, a 13 × 6 coefficient matrix is shown to reproduce the solution with sufficient accuracy. The proposed methodology is expected to find applications to parameter variation studies, uncertainty analysis, inverse problems and optimal design. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Parallel computing of high-speed compressible flows using a node-based finite-element method

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2003
T. Fujisawa
Abstract An efficient parallel computing method for high-speed compressible flows is presented. The numerical analysis of flows with shocks requires very fine computational grids and grid generation requires a great deal of time. In the proposed method, all computational procedures, from the mesh generation to the solution of a system of equations, can be performed seamlessly in parallel in terms of nodes. Local finite-element mesh is generated robustly around each node, even for severe boundary shapes such as cracks. The algorithm and the data structure of finite-element calculation are based on nodes, and parallel computing is realized by dividing a system of equations by the row of the global coefficient matrix. The inter-processor communication is minimized by renumbering the nodal identification number using ParMETIS. The numerical scheme for high-speed compressible flows is based on the two-step Taylor,Galerkin method. The proposed method is implemented on distributed memory systems, such as an Alpha PC cluster, and a parallel supercomputer, Hitachi SR8000. The performance of the method is illustrated by the computation of supersonic flows over a forward facing step. The numerical examples show that crisp shocks are effectively computed on multiprocessors at high efficiency. Copyright © 2003 John Wiley & Sons, Ltd. [source]

A practical determination strategy of optimal threshold parameter for matrix compression in wavelet BEM

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2003
Kazuhiro Koro
Abstract A practical strategy is developed to determine the optimal threshold parameter for wavelet-based boundary element (BE) analysis. The optimal parameter is determined so that the amount of storage (and computational work) is minimized without reducing the accuracy of the BE solution. In the present study, the Beylkin-type truncation scheme is used in the matrix assembly. To avoid unnecessary integration concerning the truncated entries of a coefficient matrix, a priori estimation of the matrix entries is introduced and thus the truncated entries are determined twice: before and after matrix assembly. The optimal threshold parameter is set based on the equilibrium of the truncation and discretization errors. These errors are estimated in the residual sense. For Laplace problems the discretization error is, in particular, indicated with the potential's contribution ,c, to the residual norm ,R, used in error estimation for mesh adaptation. Since the normalized residual norm ,c,/,u, (u: the potential components of BE solution) cannot be computed without main BE analysis, the discretization error is estimated by the approximate expression constructed through subsidiary BE calculation with smaller degree of freedom (DOF). The matrix compression using the proposed optimal threshold parameter enables us to generate a sparse matrix with O(N1+,) (0,,<1) non-zero entries. Although the quasi-optimal memory requirements and complexity are not attained, the compression rate of a few per cent can be achieved for N,1000. Copyright © 2003 John Wiley & Sons, Ltd. [source]

An efficient diagonal preconditioner for finite element solution of Biot's consolidation equations

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2002
K. K. Phoon
Abstract Finite element simulations of very large-scale soil,structure interaction problems (e.g. excavations, tunnelling, pile-rafts, etc.) typically involve the solution of a very large, ill-conditioned, and indefinite Biot system of equations. The traditional preconditioned conjugate gradient solver coupled with the standard Jacobi (SJ) preconditioner can be very inefficient for this class of problems. This paper presents a robust generalized Jacobi (GJ) preconditioner that is extremely effective for solving very large-scale Biot's finite element equations using the symmetric quasi-minimal residual method. The GJ preconditioner can be formed, inverted, and implemented within an ,element-by-element' framework as readily as the SJ preconditioner. It was derived as a diagonal approximation to a theoretical form, which can be proven mathematically to possess an attractive eigenvalue clustering property. The effectiveness of the GJ preconditioner over a wide range of soil stiffness and permeability was demonstrated numerically using a simple three-dimensional footing problem. This paper casts a new perspective on the potentialities of the simple diagonal preconditioner, which has been commonly perceived as being useful only in situations where it can serve as an approximate inverse to a diagonally dominant coefficient matrix. Copyright © 2002 John Wiley & Sons, Ltd. [source]

Orthogonality of modal bases in hp finite element models

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2007
V. Prabhakar
Abstract In this paper, we exploit orthogonality of modal bases (SIAM J. Sci. Comput. 1999; 20:1671,1695) used in hp finite element models. We calculate entries of coefficient matrix analytically without using any numerical integration, which can be computationally very expensive. We use properties of Jacobi polynomials and recast the entries of the coefficient matrix so that they can be evaluated analytically. We implement this in the context of the least-squares finite element model although this procedure can be used in other finite element formulations. In this paper, we only develop analytical expressions for rectangular elements. Spectral convergence of the L2 least-squares functional is verified using exact solution of Kovasznay flow. Numerical results for transient flow over a backward-facing step are also presented. We also solve steady flow past a circular cylinder and show the reduction in computational cost using expressions developed herein. Copyright © 2007 John Wiley & Sons, Ltd. [source]

A new symmetry-preserving Cartesian-grid method for computing flow past arbitrarily shaped objects

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 8-9 2005
Marc Dröge
Abstract This paper deals with a numerical method for solving the unsteady, incompressible Navier,Stokes equations in domains of arbitrarily shaped boundaries, where the boundary is represented using the Cartesian-grid approach. We introduce a novel cut-cell discretization, which preserves the symmetry of convection and diffusion. That is, convection is discretized by a skew-symmetric operator and diffusion is approximated by a symmetric, positive-definite coefficient matrix. The resulting semi-discrete (continuous in time) system conserves the kinetic energy if the dissipation is turned off; the energy decreases if dissipation is turned on. The method is successfully tested for an incompressible, unsteady flow around a circular cylinder at Re=100. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Application of the preconditioned GMRES to the Crank-Nicolson finite-difference time-domain algorithm for 3D full-wave analysis of planar circuits

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS, Issue 6 2008
Y. Yang
Abstract The increase of the time step size significantly deteriorates the property of the coefficient matrix generated from the Crank-Nicolson finite-difference time-domain (CN-FDTD) method. As a result, the convergence of classical iterative methods, such as generalized minimal residual method (GMRES) would be substantially slowed down. To address this issue, this article mainly concerns efficient computation of this large sparse linear equations using preconditioned generalized minimal residual (PGMRES) method. Some typical preconditioning techniques, such as the Jacobi preconditioner, the sparse approximate inverse (SAI) preconditioner, and the symmetric successive over-relaxation (SSOR) preconditioner, are introduced to accelerate the convergence of the GMRES iterative method. Numerical simulation shows that the SSOR preconditioned GMRES method can reach convergence five times faster than GMRES for some typical structures. © 2008 Wiley Periodicals, Inc. Microwave Opt Technol Lett 50: 1458,1463, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.23396 [source]

A multilevel Crout ILU preconditioner with pivoting and row permutation

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 10 2007
Jan MayerArticle first published online: 4 SEP 200
Abstract In this paper, we present a new incomplete LU factorization using pivoting by columns and row permutation. Pivoting by columns helps to avoid small pivots and row permutation is used to promote sparsity. This factorization is used in a multilevel framework as a preconditioner for iterative methods for solving sparse linear systems. In most multilevel incomplete ILU factorization preconditioners, preprocessing (scaling and permutation of rows and columns of the coefficient matrix) results in further improvements. Numerical results illustrate that these preconditioners are suitable for a wide variety of applications. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Combination of Jacobi,Davidson and conjugate gradients for the partial symmetric eigenproblem

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 1 2002
Y. Notay
Abstract To compute the smallest eigenvalues and associated eigenvectors of a real symmetric matrix, we consider the Jacobi,Davidson method with inner preconditioned conjugate gradient iterations for the arising linear systems. We show that the coefficient matrix of these systems is indeed positive definite with the smallest eigenvalue bounded away from zero. We also establish a relation between the residual norm reduction in these inner linear systems and the convergence of the outer process towards the desired eigenpair. From a theoretical point of view, this allows to prove the optimality of the method, in the sense that solving the eigenproblem implies only a moderate overhead compared with solving a linear system. From a practical point of view, this allows to set up a stopping strategy for the inner iterations that minimizes this overhead by exiting precisely at the moment where further progress would be useless with respect to the convergence of the outer process. These results are numerically illustrated on some model example. Direct comparison with some other eigensolvers is also provided. Copyright © 2001 John Wiley & Sons, Ltd. [source]

Analysis of algebraic systems arising from fourth-order compact discretizations of convection-diffusion equations

MGM Optimal convergence for certain (multilevel) structured linear systems

PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2003
Antonio Aricó Dr.
We present a multigrid algorithm to solve linear systems whose coefficient metrices belongs to circulant, Hartley or , multilevel algebras and are generated by a nonnegative multivariate polynomial f. It is known that these matrices are banded (with respect to their multilevel structure) and their eigenvalues are obtained by sampling f on uniform meshes, so they are ill-conditioned (or singular, and need some corrections) whenever f takes the zero value. We prove the proposed metod to be optimal even in presence of ill-conditioning: if the multilevel coefficient matrix has dimension ni at level i, i = 1, , , d, then only ni operations are required on each iteration, but the convergence rate keeps constant with respect to N(n) as it depends only on f. The algorithm can be extended to multilevel Toeplitz matrices too. [source]

LMI based stability and stabilization of second-order linear repetitive processes,

ASIAN JOURNAL OF CONTROL, Issue 2 2010
Pawel Dabkowski
Abstract This paper develops new results on the stability and control of a class of linear repetitive processes described by a second-order matrix discrete or differential equation. These are developed by transformation of the second-order dynamics to those of an equivalent first-order descriptor state-space model, thus avoiding the need to invert a possibly ill-conditioned leading coefficient matrix in the original model. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source]

Least-square-based radial basis collocation method for solving inverse problems of Laplace equation from noisy data

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2010
Xian-Zhong Mao
Abstract The inverse problem of 2D Laplace equation involves an estimation of unknown boundary values or the locations of boundary shape from noisy observations on over-specified boundary or internal data points. The application of radial basis collocation method (RBCM), one of meshless and non-iterative numerical schemes, directly induces this inverse boundary value problem (IBVP) to a single-step solution of a system of linear algebraic equations in which the coefficients matrix is inherently ill-conditioned. In order to solve the unstable problem observed in the conventional RBCM, an effective procedure that builds an over-determined linear system and combines with least-square technique is proposed to restore the stability of the solution in this paper. The present work investigates three examples of IBVPs using over-specified boundary conditions or internal data with simulated noise and obtains stable and accurate results. It underlies that least-square-based radial basis collocation method (LS-RBCM) poses a significant advantage of good stability against large noise levels compared with the conventional RBCM. Copyright © 2010 John Wiley & Sons, Ltd. [source]