A fundamental solution method for inverse heat conduction problem

Hon, Y.C.; Wei, Ting

doi:10.1016/s0955-7997(03)00102-4

Cited by 187 publications

(93 citation statements)

References 16 publications

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“…26,41 MFS approximates the solution of a PDE by a linear combination of fundamental solutions of the governing partial differential operator, 27 which for ECGI is the Laplacian operator ▽². The formulation of MFS for a▽² boundary value problem and Cauchy problem is described in the Appendix; its implementation in ECGI is described below.…”

Section: Formulating the Methods Of Fundamental Solutions For Ecgimentioning

confidence: 99%

Application of the Method of Fundamental Solutions to Potential-based Inverse Electrocardiography

2006

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Potential-based inverse electrocardiography is a method for the noninvasive computation of epicardial potentials from measured body surface electrocardiographic data. From the computed epicardial potentials, epicardial electrograms and isochrones (activation sequences), as well as repolarization patterns can be constructed. We term this noninvasive procedure Electrocardiographic Imaging (ECGI). The method of choice for computing epicardial potentials has been the Boundary Element Method (BEM) which requires meshing the heart and torso surfaces and optimizing the mesh, a very time-consuming operation that requires manual editing. Moreover, it can introduce mesh-related artifacts in the reconstructed epicardial images. Here we introduce the application of a meshless method, the Method of Fundamental Solutions (MFS) to ECGI. This new approach that does not require meshing is evaluated on data from animal experiments and human studies, and compared to BEM. Results demonstrate similar accuracy, with the following advantages: 1. Elimination of meshing and manual mesh optimization processes, thereby enhancing automation and speeding the ECGI procedure. 2. Elimination of mesh-induced artifacts. 3. Elimination of complex singular integrals that must be carefully computed in BEM. 4. Simpler implementation. These properties of MFS enhance the practical application of ECGI as a clinical diagnostic tool.

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Section: Formulating the Methods Of Fundamental Solutions For Ecgimentioning

confidence: 99%

Application of the Method of Fundamental Solutions to Potential-based Inverse Electrocardiography

2006

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“…There has been considerable interest in methods for solving inverse diffusion problems in recent years [11][12][13][14][15]. The method that will be applied to the SIMS quantification problem in this paper is the Operator-Splitting Method, developed for the inverse solution of general diffusion problems in Kirkup and Wadsworth [11].…”

Section: Quantification Methodsmentioning

confidence: 99%

The inverse solution of the atomic mixing equations by an operator-splitting method

Kirkup

Yazdani

Aspey

et al. 2014

Applied Mathematical Modelling

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The quantification problem of recovering the original material distribution from secondary ion mass spectrometry (SIMS) data is considered in this paper. It is an inverse problem, is ill-posed and hence it requires a special technique for its solution. The quantification problem is essentially an inverse diffusion or (classically) a backward heat conduction problem. In this paper an operator-splitting method (that is proposed in a previous paper by the first author for the solution of inverse diffusion problems) is developed for the solution of the problem of recovering the original structure from the SIMS data. A detailed development of the quantification method is given and it is applied to typical data to demonstrate its effectiveness.

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“…Recent developments of meshless computational methods for solving real physical problems include the use of the fundamental solution as basis function (strong form) for solving inverse boundary determination and inverse heat conduction problems [14,13]. A good review on the method of fundamental solutions (MFS) can be found from [11].…”

Section: Symmetric Meshless Kernel Methodsmentioning

confidence: 99%