Local and Dimension Adaptive Sparse Grid Interpolation and Quadrature

@article{Jakeman2011LocalAD,
  title={Local and Dimension Adaptive Sparse Grid Interpolation and Quadrature},
  author={John D. Jakeman and Stephen G. Roberts},
  journal={CoRR},
  year={2011},
  volume={abs/1110.0010}
}
In this paper we present a locally and dimension-adaptive sparse grid method for interpolation and integration of high-dimensional functions with discontinuities. The proposed algorithm combines the strengths of the generalised sparse grid algorithm and hierarchical surplus-guided local adaptivity. A high-degree basis is used to obtain a high-order method which, given sufficient smoothness, performs significantly better than the piecewise-linear basis. The underlying generalised sparse grid… CONTINUE READING
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