DASHMM Accelerated Adaptive Fast Multipole Poisson-Boltzmann Solver on Distributed Memory Architecture

Zhang, Bo; DeBuhr, Jackson; Niedzielski, D.; Mayolo, Silvio; Lu, Benzhuo; Sterling, Thomas

doi:10.4208/cicp.oa-2018-0098

Cited by 7 publications

(8 citation statements)

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“…The programming effort required to implement a second formulation would have been a good reason. In our experiments, the exterior version used by Lu and coworkers [19,20,13] took about half as many iterations to converge than the interior version-a sizable advantage. This led us to study the properties of the two variants of the derivative formulation in more detail.…”

Section: Matrix Conditioning Of Two Derivative Formulationsmentioning

confidence: 84%

“…Starting from electrostatic theory, this leads to a mathematical model based on the Poisson-Boltzmann equation, and widely used to compute mean-field electrostatic potentials and solvation free energies. Poisson-Boltzmann solvers have been numerically implemented using finite difference [3,4], finite element [4,5,6], boundary element [7,8,9,10], and (semi) analytical [11,12] methods, scaling up to problems as large as virus capsids [13,14].…”

Section: Introductionmentioning

confidence: 99%

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High-productivity, high-performance workflow for virus-scale electrostatic simulations with Bempp-Exafmm

Wang¹,

Cooper²,

Betcke³

et al. 2021

Preprint

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Biomolecular electrostatics is key in protein function and the chemical processes affecting it. Implicit-solvent models expressed by the Poisson-Boltzmann (PB) equation can provide insights with less computational power than full atomistic models, making large-system studies-at the scale of viruses, for example-accessible to more researchers. This paper presents a high-productivity and high-performance computational workflow combining Exafmm, a fast multipole method (FMM) library, and Bempp, a Galerkin boundary element method (BEM) package. It integrates an easy-to-use Python interface with well-optimized computational kernels that are written in compiled languages. Researchers can run PB simulations interactively via Jupyter notebooks, enabling faster prototyping and analyzing. We provide results that showcase the capability of the software, confirm correctness, and evaluate its performance with problem sizes between 8,000 and 2 million boundary elements. A study comparing two variants of the boundary integral formulation in regards to algebraic conditioning showcases the power of this interactive computing platform to give useful answers with just a few lines of code. As a form of solution verification, mesh refinement studies with a spherical geometry as well as with a real biological structure (5PTI) confirm convergence at the expected 1/N rate, for N boundary elements. Performance results include timings, breakdowns, and computational complexity. Exafmm offers evaluation speeds of just a few seconds for tens of millions of points, and O(N ) scaling. This allowed computing the solvation free energy of a Zika virus, represented by 1.6 million atoms and 10 million boundary elements, at 80-min runtime on a single compute node (dual 20-core Intel Xeon Gold 6148). All results in the paper are presented with utmost care for reproducibility. Readers can find input data (meshes and pqr files) in a Zenodo archive, Jupyter notebooks and secondary data necessary to reproduce all the figures in the paper's GitHub repository at https://github.com/barbagroup/bempp_exafmm_paper/, and all the software in version-controlled repositories under permissive standard licenses.

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Section: Matrix Conditioning Of Two Derivative Formulationsmentioning

confidence: 84%

Section: Introductionmentioning

confidence: 99%

High-productivity, high-performance workflow for virus-scale electrostatic simulations with Bempp-Exafmm

Wang¹,

Cooper²,

Betcke³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…The solution of Poisson's equation plays an essential role in scientific computing as well as many physical and engineering applications such as molecular simulations, electric structure calculations, computational astrophysics, and fluid dynamics for both particle simulations [1][2][3][4] and continuum-theory calculations [5][6][7][8]. The development of efficient method for the Poisson's equation in these fields remains an important theme for simulations using high-performance computing.…”

Section: Introductionmentioning

confidence: 99%

A High-Accurate Fast Poisson Solver Based on Harmonic Surface Mapping Algorithm

Liang¹

2022

CiCP

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Poisson's equations in a cuboid are frequently solved in many scientific and engineering applications such as electric structure calculations, molecular dynamics simulations and computational astrophysics. In this paper, a fast and highly accurate algorithm is presented for the solution of the Poisson's equation in a cuboidal domain with boundary conditions of mixed type. This so-called harmonic surface mapping algorithm is a meshless algorithm which can achieve a desired order of accuracy by evaluating a body convolution of the source and the free-space Green's function within a sphere containing the cuboid, and another surface integration over the spherical surface. Numerical quadratures are introduced to approximate the integrals, resulting in the solution represented by a summation of point sources in free space, which can be accelerated by means of the fast multipole algorithm. The complexity of the algorithm is linear to the number of quadrature points, and the convergence rate can be arbitrarily high even when the source term is a piecewise continuous function.

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“…Then, the molecular surface is accurately represented, making BEM favorable for high precision simulations. 14 However, BEM generates dense matrices that need fast methods to access large problems, such as fast multipole methods, [18][19][20][21] treecodes, 22,23 or hierarchical matrices. 24,25 Numerical approximations to the PBE often have large error.…”

Section: Introductionmentioning

confidence: 99%

Efficient mesh refinement for the Poisson‐Boltzmann equation with boundary elements

2021

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The Poisson-Boltzmann equation is a widely used model to study electrostatics in molecular solvation. Its numerical solution using a boundary integral formulation requires a mesh on the molecular surface only, yielding accurate representations of the solute, which is usually a complicated geometry. Here, we utilize adjoint-based analyses to form two goal-oriented error estimates that allow us to determine the contribution of each discretization element (panel) to the numerical error in the solvation free energy. This information is useful to identify high-error panels to then refine them adaptively to find optimal surface meshes. We present results for spheres and real molecular geometries, and see that elements with large error tend to be in regions where there is a high electrostatic potential. We also find that even though both estimates predict different total errors, they have similar performance as part of an adaptive mesh refinement scheme. Our test cases suggest that the adaptive mesh refinement scheme is very effective, as we are able to reduce the error one order of magnitude by increasing the mesh size less than 20% and come out to be more efficient than uniform refinement when computing error estimations. This result sets the basis toward efficient automatic mesh refinement schemes that produce optimal meshes for solvation energy calculations.

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DASHMM Accelerated Adaptive Fast Multipole Poisson-Boltzmann Solver on Distributed Memory Architecture

Cited by 7 publications

References 0 publications

High-productivity, high-performance workflow for virus-scale electrostatic simulations with Bempp-Exafmm

High-productivity, high-performance workflow for virus-scale electrostatic simulations with Bempp-Exafmm

A High-Accurate Fast Poisson Solver Based on Harmonic Surface Mapping Algorithm

Efficient mesh refinement for the Poisson‐Boltzmann equation with boundary elements

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