The Experts below are selected from a list of 279 Experts worldwide ranked by ideXlab platform
Ion Păvăloiu - One of the best experts on this subject based on the ideXlab platform.
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SYNASC - On a Steffensen Type Method
Ninth International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC 2007), 2007Co-Authors: Ion Păvăloiu, Emil CatinasAbstract:We study a general Steffensen type method based on the Inverse Interpolation Lagrange polynomial of second degree. We show how the auxiliary functions may be constructed and we analyze some conditions on them which lead to monotone approximations. We obtain some local convergence results, which are illustrated by some numerical examples.
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On a Steffensen Type Method
Ninth International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC 2007), 2007Co-Authors: Ion Păvăloiu, Emil CatinasAbstract:We study a general Steffensen type method based on the Inverse Interpolation Lagrange polynomial of second degree. We show how the auxiliary functions may be constructed and we analyze some conditions on them which lead to monotone approximations. We obtain some local convergence results, which are illustrated by some numerical examples.
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Bilateral approximations of the roots of scalar equations by Lagrange-Aitken-Steffensen method of order three
2006Co-Authors: Ion PăvăloiuAbstract:We study the monotone convergence of two general methods of Aitken-Steffenssen type. These methods are obtained from the Lagrange Inverse Interpolation polynomial of degree two, having controlled nodes. The obtained results provide information on controlling the errors at each iteration step.
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On a Steffensen-Hermite type method for approximating the solutions of nonlinear equations
2006Co-Authors: Ion PăvăloiuAbstract:It is well known that the Steffensen and Aitken-Steffensen type methods are obtained from the chord method, using controlled nodes. The chord method is an interpolatory method, with two distinct nodes. Using this remark, the Steffensen and Aitken-Steffensen methods have been generalized using interpolatory methods obtained from the Inverse Interpolation polynomial of Lagrange or Hermite type. In this paper we study the convergence and efficiency of some Steffensen type methods which are obtained from the Inverse interpolatory polynomial of Hermite type with two controlled nodes.
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Local convergence of general Steffensen type methods
2004Co-Authors: Ion PăvăloiuAbstract:We study the local convergence of a generalized Steffensen method. We show that this method substantially improves the convergence order of the classical Steffensen method. The convergence order of our method is greater or equal to the number of the controlled nodes used in the Lagrange-type Inverse Interpolation, which, in its turn, is substantially higher than the convergence orders of the Lagrange type Inverse Interpolation with uncontrolled nodes (since their convergence order is at most \(2\)).
Wen Chen - One of the best experts on this subject based on the ideXlab platform.
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A regularized approach evaluating origin intensity factor of singular boundary method for Helmholtz equation with high wavenumbers
Engineering Analysis With Boundary Elements, 2019Co-Authors: Junpu Li, Zhuo-jia Fu, Wen ChenAbstract:Abstract Evaluation of the origin intensity factor of the singular boundary method for Helmholtz equation with high wavenumbers has been a difficult task for a long time. In this study, a regularized approach is provided to bypass this limitation. The core idea of the subtraction and adding-back technique is to substitute an artificially constructed general solution of the Helmholtz equation into the boundary integral equation or the hyper boundary integral equation to evaluate the non-singular expressions of the fundamental solutions at origin. The core difficulty is to derive the appropriate artificially constructed general solution. The regularized approach avoids the unstable Inverse Interpolation and has strict mathematical derivation process. Therefore, it is easy-to-program and free of mesh dependency. Numerical experiments show that the proposed technique can be used successfully to avoid singularity and hyper singularity difficulties encountered in the boundary element method and the singular boundary method.
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Evaluating the Origin Intensity Factor in the Singular Boundary Method for Three-Dimensional Dirichlet Problems
Advances in Applied Mathematics and Mechanics, 2017Co-Authors: Wen Chen, Alexander H.-d. ChengAbstract:In this paper, a new formulation is proposed to evaluate the origin intensity factors (OIFs) in the singular boundary method (SBM) for solving 3D potential problems with Dirichlet boundary condition. The SBM is a strong-form boundary discretization collocation technique and is mathematically simple, easy-to-program, and free of mesh. The crucial step in the implementation of the SBM is to determine the OIFs which isolate the singularities of the fundamental solutions. Traditionally, the Inverse Interpolation technique (IIT) is adopted to calculate the OIFs on Dirichlet boundary, which is time consuming for large-scale simulation. In recent years, the new methodology has been developed to efficiently calculate the OIFs on Neumann boundary, but the Dirichlet problem remains an open issue. This study employs the subtracting and adding-back technique based on the integration of the fundamental solution over the whole boundary to develop a new formulation of the OIFs on 3D Dirichlet boundary. Several problems with varied domain shapes and boundary conditions are carried out to validate the effectiveness and feasibility of the proposed scheme in comparison with the SBM based on Inverse Interpolation technique, the method of fundamental solutions, and the boundary element method.
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Explicit empirical formula evaluating original intensity factors of singular boundary method for potential and Helmholtz problems
Engineering Analysis With Boundary Elements, 2016Co-Authors: Junpu Li, Wen Chen, Zhuo-jia FuAbstract:Abstract This short communication proposes two new explicit empirical formulas to determine the original intensity factors on Neumann and Dirichlet boundary in the singular boundary method (SBM) solution of 2D and 3D potential and Helmholtz problems. Without numerical integration and subtracting and adding-back technique, the original intensity factors can be obtained directly by implementing the proposed explicit empirical formulas. The numerical investigations show that the SBM with these new explicit empirical formulas can provide the accurate solutions of several benchmark examples in comparison with the analytical, Boundary element method (BEM) and Regularized meshless method (RMM) solutions. In most cases, the present SBM with empirical formulas yields the similar numerical accuracy as the BEM and the SBM in which the original intensity factors are evaluated by the other time-consuming approaches. It is worthy of noting that the empirical formula costs far less CPU and storage requirements at the same number of boundary nodes and performs more stably than the Inverse Interpolation technique in the SBM.
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Singular boundary method using time-dependent fundamental solution for transient diffusion problems
Engineering Analysis With Boundary Elements, 2016Co-Authors: Wen Chen, Fajie WangAbstract:Abstract This paper documents the first attempt to apply the singular boundary method (SBM) with time-dependent fundamental solution to transient diffusion equations. An Inverse Interpolation technique is introduced to determine the origin intensity factor of the SBM. The scheme is mathematically simple, easy-to-program, truly boundary-only, free of integration and mesh. Several examples, especially three-dimensional (3D) cases, are provided to verify time-dependent SBM strategy. The numerical results clearly demonstrate its great potential.
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Singular boundary method for modified Helmholtz equations
Engineering Analysis With Boundary Elements, 2014Co-Authors: Wen Chen, Jinyang Zhang, Zhuo-jia FuAbstract:This study makes the first attempt to apply a recent strong-form boundary collocation method using the singular fundamental solutions, namely the singular boundary method (SBM), to 2D and 3D modified Helmholtz equations. By the desingularization of subtracting and adding-back technique, the corresponding nonsingular SBM formulations are derived based on null-field integral equations and an Inverse Interpolation technique. Numerical demonstrations show the feasibility and accuracy of the present SBM in some benchmark problems.
Chuanzeng Zhang - One of the best experts on this subject based on the ideXlab platform.
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singular boundary method for solving plane strain elastostatic problems
International Journal of Solids and Structures, 2011Co-Authors: Yan Gu, Wen Chen, Chuanzeng ZhangAbstract:This study documents the first attempt to apply the singular boundary method (SBM), a novel boundary only collocation method, to two-dimensional (2D) elasticity problems. Unlike the method of fundamental solutions (MFS), the source points coincide with the collocation points on the physical boundary by using an Inverse Interpolation technique to regularize the singularity of the fundamental solution of the equation governing the problems of interest. Three benchmark elasticity problems are tested to demonstrate the feasibility and accuracy of the proposed method through detailed comparisons with the MFS, boundary element method (BEM), and finite element method (FEM).
Adolf Pfefferbaum - One of the best experts on this subject based on the ideXlab platform.
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volume reconstruction by Inverse Interpolation application to interleaved mr motion correction
Medical Image Computing and Computer-Assisted Intervention, 2008Co-Authors: Torsten Rohlfing, Martin H Rademacher, Adolf PfefferbaumAbstract:We introduce in this work a novel algorithm for volume reconstruction from data acquired on an irregular grid, e.g., from multiple co-registered images. The algorithm, which is based on an Inverse Interpolation formalism, is superior to other methods in particular when the input images have lower spatial resolution than the reconstructed image. Local intensity bounds are enforced by an L-BFGS-B optimizer, regularize the reconstruction problem, and preserve the intensity distribution of the input images. We demonstrate the usefulness of our method by applying it to retrospective motion correction in interleaved MR images.
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MICCAI (1) - Volume Reconstruction by Inverse Interpolation: Application to Interleaved MR Motion Correction
Medical image computing and computer-assisted intervention : MICCAI ... International Conference on Medical Image Computing and Computer-Assisted Inte, 2008Co-Authors: Torsten Rohlfing, Martin H Rademacher, Adolf PfefferbaumAbstract:We introduce in this work a novel algorithm for volume reconstruction from data acquired on an irregular grid, e.g., from multiple co-registered images. The algorithm, which is based on an Inverse Interpolation formalism, is superior to other methods in particular when the input images have lower spatial resolution than the reconstructed image. Local intensity bounds are enforced by an L-BFGS-B optimizer, regularize the reconstruction problem, and preserve the intensity distribution of the input images. We demonstrate the usefulness of our method by applying it to retrospective motion correction in interleaved MR images.
Emil Catinas - One of the best experts on this subject based on the ideXlab platform.
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SYNASC - On a Steffensen Type Method
Ninth International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC 2007), 2007Co-Authors: Ion Păvăloiu, Emil CatinasAbstract:We study a general Steffensen type method based on the Inverse Interpolation Lagrange polynomial of second degree. We show how the auxiliary functions may be constructed and we analyze some conditions on them which lead to monotone approximations. We obtain some local convergence results, which are illustrated by some numerical examples.
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On a Steffensen Type Method
Ninth International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC 2007), 2007Co-Authors: Ion Păvăloiu, Emil CatinasAbstract:We study a general Steffensen type method based on the Inverse Interpolation Lagrange polynomial of second degree. We show how the auxiliary functions may be constructed and we analyze some conditions on them which lead to monotone approximations. We obtain some local convergence results, which are illustrated by some numerical examples.
