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 arbitrarilyshaped domains using the MADNESS (multiresolution adaptive numerical environment for scientific simulation) package for adaptive computation with multiresolution algorithms. We begin by implementing a previouslyreported 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 nonphysical solutions with zero first and second derivatives at the boundary. This excessive smoothness leads to large numerical cancellation and confounds the dynamicallyadaptive, multiresolution algorithms inside { t MADNESS}. We thus generalize the diffuse domain approximation, producing a formalism that demonstrates firstorder convergence in both near and farfield 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 
Standard Articles
1 Publication describing the Software, including 1 Publication in zbMATH  Year 

Solving PDEs in irregular geometries with multiresolution methods. I: Embedded Dirichlet boundary conditions. Zbl 1263.65122 Reuter, Matthew G.; Hill, Judith C.; Harrison, Robert J. 
2012

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Referenced by 34 Authors
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Referenced in 6 Serials
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