Abstract
AbstractIn this paper, we present a scattered data approximation method for detecting and approximating the discontinuities of a bivariate function and its gradient. The new algorithm is based on partition of unity, polyharmonic kernel interpolation, and principal component analysis. Localized polyharmonic interpolation in partition of unity setting is applied for detecting a set of fault points on or close to discontinuity curves. Then a combination of partition of unity and principal component regression is used to thinning the detected points by moving them approximately on the fault curves. Finally, an ordered subset of these narrowed points is extracted and a parametric spline interpolation is applied to reconstruct the fault curves. A selection of numerical examples with different behaviors and an application for solving scalar conservation law equations illustrate the performance of the algorithm.
Funder
Iran National Science Foundation
Publisher
Springer Science and Business Media LLC
Cited by
3 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献