Journal Article10.4208/AAMM.2014.M611
Meshless Collocation Method for Inverse Source Identification Problems
Fuzhang Wang,Zhaoxing Ma +1 more
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TL;DR: In this paper, a meshless scheme is proposed for inverse source identification problems of Helmholtz-type equations, which can determine smooth source terms from partially accessible boundary measurements with accurate results.
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Abstract: A novel meshless scheme is proposed for inverse source identification problems of Helmholtz-type equations. It is formulated by the non-singular general solutions of the Helmholtz-type equations augmented with radial basis functions. Under this meshless scheme, we can determine smooth source terms from partially accessible boundary measurements with accurate results. Numerical examples are presented to verify validity and accuracy of the present scheme. It is demonstrated that the present scheme is simple, accurate, stable and computationally efficient for inverse smooth source identification problems.
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Citations
Learning solutions to the source inverse problem of wave equations using LS-SVM
TL;DR: In this article, a method based on least squares support vector machines (LS-SVM) was proposed to solve the source inverse problem of wave equations, which provides a closed form approximate solution which satisfies the boundary conditions and the initial conditions.
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The Quasi-Optimal Radial Basis Function Collocation Method: A Technical Note
TL;DR: In this article, a coupled radial basis function based on the infinitely smooth radial basis functions and the conical spline was proposed to achieve an accurate and stable numerical solution, while the shape parameter values are almost independent.
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