Article citationsMore>>

Ammar, A. and Chinesta, F. (2008) Circumventing Curse of Dimensionality in the Solution of Highly Multidimensional Models Encountered in Quantum Mechanics Using Meshfree Finite Sums Decompositions. In: Griebel, M. and Schweitzer, M.A., Eds., Meshfree Methods for Partial Differential Equations IV, Springer, Berlin, 1-17.
https://doi.org/10.1007/978-3-540-79994-8_1

has been cited by the following article:

• TITLE: Multiwavelet Boundary Element Method for Cavities Admitting Many NURBS Patches

  AUTHORS: Maharavo Randrianarivony

  KEYWORDS: Wavelet, Patch, NURBS, Connolly, Modeling

  JOURNAL NAME: Modeling and Numerical Simulation of Material Science, Vol.6 No.4, December 30, 2016

  ABSTRACT: We consider the modeling and simulation by means of multiwavelets on many patches. Our focus is on molecular surfaces which are represented in the form of Solvent Excluded Surfaces that are featured by smooth blendings between the constituting atoms. The wavelet bases are constructed on the unit square which maps bijectively onto the patches embedded in the space. The cavity which designates the surface bounding a molecular model is acquired from the nuclei coordinates and the Van-der-Waals radii. We use multi-wavelets for which the wavelet basis functions are organized hierarchically on several levels. Our assembly of the linear system is accomplished by using a hierarchical tree which enables the treatment of large molecules admitting thousands of patches. Along with the patch construction, some wavelet simulation outcomes which are applied to realistic patches are reported.