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MADNESS

swMATH ID: 6887
Software Authors: Reuter, Matthew G.; Hill, Judith C.; Harrison, Robert J.
Description: Solving PDEs in irregular geometries with multiresolution methods. I: Embedded Dirichlet boundary conditions In this work, we develop and analyze a formalism for solving boundary value problems in arbitrarily-shaped domains using the MADNESS (multiresolution adaptive numerical environment for scientific simulation) package for adaptive computation with multiresolution algorithms. We begin by implementing a previously-reported diffuse domain approximation for embedding the domain of interest into a larger domain (Li et al., 2009 [1]). Numerical and analytical tests both demonstrate that this approximation yields non-physical solutions with zero first and second derivatives at the boundary. This excessive smoothness leads to large numerical cancellation and confounds the dynamically-adaptive, multiresolution algorithms inside { t MADNESS}. We thus generalize the diffuse domain approximation, producing a formalism that demonstrates first-order convergence in both near- and far-field errors. We finally apply our formalism to an electrostatics problem from nanoscience with characteristic length scales ranging from 0.0001 to 300 nm.
Homepage: http://www.csm.ornl.gov/ccsg/html/projects/madness.html
Keywords: multiresolution analysis; domain embedding techniques; electrostatics
Related Software: BLIS; TTC; P3DFFT; TensorFlow; HPTT; Eigen; fbfft; CTF; cuDNN; AUGEM; Tensorlab; Algorithm 679; Algorithm 862; MKL; NWChem; TensorToolbox; GitHub; OpenDX; TiledArray; CHARM++
Referenced in: 6 Publications

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