Meshfree Approximation Methods with Matlab

By Gregory E. Fasshauer. Interdisciplinary Mathematical Sciences, 2007

1,879 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/498d27f4d3a616beb058333e410811808f7fe46d

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Citations in the corpus

Solving PDEs with radial basis functions * (2015, methodology): “Several different short proofs for this are available (Fasshauer 2007, Fornberg and Flyer 2015b, Powell 1992).”
Approximation of eigenfunctions in kernel-based spaces (2014, unknown): “Details can be retrieved from the monographs [2, 27, 7] and the surveys [1, 25].”
Improved Kansa RBF method for the solution of nonlinear boundary value problems (2018, background): “The RBFs r2n−1 are also known as the radial power RBFs [9] and may be used for problems in all (both even and odd) dimensions.”
Exact imposition of boundary conditions with distance functions in physics-informed deep neural networks (2021, methodology): “First, we present a few connections of prior work on ﬁnite elements and partition-of-unity meshfree methods to better understand and place the PINN approximation and its use to solve PDEs.”
Three-Dimensional Modelling of Geological Surfaces Using Generalized Interpolation with Radial Basis Functions (2014, methodology): “It is important to note that numerical techniques, such as leave one out cross validation (LOOCV), are available to optimally choose the best RBF and, if applicable, the shape parameter ε, using a particular dataset (Fasshauer 2007b; Scheuerer et al. 2013).”
On the role of polynomials in RBF-FD approximations: II. Numerical solution of elliptic PDEs (2017, background): “There are many choices of RBFs φ(r) that can be used [7, 14].”
Gaussian RBF-FD weights and its corresponding local truncation errors (2012, unknown): “1 Introduction Radial basis functions (RBFs) were first used as an efficient technique for interpolation of multidimensional scattered data [7].”