BEM++ : Cool new library for boundary-element method (BEM) simulations

BEM++ offers attractive high-level interfaces for doing BEM calculations in Python and C++.

Currently it supports Galerkin BEM for the Laplace, Helmholtz, and modified Helmholtz (Yukawa or linearized Poisson-Boltzmann) equations, using planar triangle boundary elements with either piecewise-constant or piecewise-linear basis functions.  Support for collocation or qualocation would be nice, and it seems like these can be implemented pretty easily.

For fast BEM, the library supports AHMED (H-matrix based) representations only; coupling BEM++ to tree codes or fast multipole methods would be really important to me in production-level work.  At the moment, I’m really just happy to have a high-quality implementation for hypersingular operators.

I’ve gotten BEM++ installed and running without much trouble at all, and I look forward to giving it a real workout over the Christmas holidays (when I’m done teaching).

Congratulations to the BEM++ team, and thanks for releasing it as open-source software under the BSD license!

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Our new paper on asymmetric solvation is out!

Pavel Jungwirth, Lee Makowski, and I have a new paper out in The Journal of Chemical Physics: “Affine-response model of molecular solvation of ions: Accurate predictions of asymmetric charging free energies.”  This paper was a whole lot of fun to think about, work on, and write.  Please e-mail me if you’d like more information on the simulations, or do not have access to the article.

Our new paper on ellipsoidal harmonics is out!

Matt Knepley and I have a new paper out in the open-access journal Computational Science and Discovery (IOP).

The article, “Computational science and re-discovery: open-source implementation of ellipsoidal harmonics for problems in potential theory,” represents a new direction for Matt’s and my continuing work on simple models for biomolecular electrostatics.  Our previous paper addressed an analysis of boundary-integral operators on the sphere, and in this work we begin to look towards the much more general case of ellipsoids.  As it turns out, implementing ellipsoidal harmonics is quite a bit trickier than implementing spherical harmonics, so we thought it would be best to double-check our work by developing TWO implementations, one in MATLAB and one in Python.  Both are freely available under BSD licenses at Matt’s bitbucket site at https://bitbucket.org/knepley/ellipsoidal-potential-theory.

Incidentally, the article was submitted to CS&D’s special issue celebrating the 20th anniversary of the Department of Energy’s Computational Science Graduate Fellowship program, which is administered by the wonderful people at the Krell Institute.  I was a fellow from 2002-2006, and consider it one of the greatest privileges I have been afforded in my life.  Eligible young researchers in computational science and engineering (currently, that means undergraduate seniors and first-year grad students) are strongly encouraged to apply!!

Our new paper on fast Poisson approximations for protein electrostatics is out!

Matt Knepley and I continue to improve the BIBEE model (boundary-integral based electrostatics estimation) using mathematical analysis of the underlying integral operator.  The newest version, published here, achieves 4% accuracy with a single fit parameter.  The authoritative version of the paper is at The Journal of Chemical Physics, but a non-typeset version is available at ArXiv.org.

We would especially like to thank my department chair, Prof. Bob Eisenberg, for his continuing support and encouragement in our quest for better implicit-solvent models.  Also, we would like to acknowledge the referee for his or her very insightful and tough comments; these led to a substantially improved paper.

Onward!