Regularization of Poisson--Boltzmann Type Equations with Singular Source Terms Using the Range-Separated Tensor Format

DOI10.1137/19M1281435zbMath1466.65180OpenAlexW3125228000WikidataQ115214741 ScholiaQ115214741MaRDI QIDQ5857619

Peter Benner, Cleophas M. Kweyu, Boris N. Khoromskij, Venera Khoromskaia, Matthias Stein

Publication date: 1 April 2021

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/19m1281435

zbMATH Keywords

Coulomb potentialPoisson-Boltzmann equationlong-range many-particle interactionsrange-separated tensor formatssummation of electrostatic potentialslow-rank tensor decompositions

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) PDEs in connection with optics and electromagnetic theory (35Q60) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Electro- and magnetostatics (78A30) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22) Boltzmann equations (35Q20)

Related Items (5)

A regularization approach for solving the super-Gaussian Poisson-Boltzmann model with heterogeneous dielectric functions ⋮ Convergence of a diffuse interface Poisson-Boltzmann (PB) model to the sharp interface PB model: a unified regularization formulation ⋮ Mathematical methods in quantum chemistry. Abstracts from the workshop held March 18--24, 2018 ⋮ On regularization of charge singularities in solving the Poisson-Boltzmann equation with a smooth solute-solvent boundary ⋮ Prospects of tensor-based numerical modeling of the collective electrostatics in many-particle systems

Uses Software

• APBS
• MPBEC

Cites Work

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• Tensor numerical methods in scientific computing
• A new box iterative method for a class of nonlinear interface problems with application in solving Poisson-Boltzmann equation
• New solution decomposition and minimization schemes for Poisson-Boltzmann equation in calculation of biomolecular electrostatics
• Grid-based lattice summation of electrostatic potentials by assembled rank-structured tensor approximation
• An aggregation-based algebraic multigrid method
• Low-rank Kronecker-product approximation to multi-dimensional nonlocal operators I. Separable approximation of multi-variate functions
• Comments on P\(^3\)M, FMM, and the Ewald method for large periodic Coulombic systems
• Continuum solvation model: Computation of electrostatic forces from numerical solutions to the Poisson-Boltzmann equation
• A two-component matched interface and boundary (MIB) regularization for charge singularity in implicit solvation
• Hierarchical tensor-product approximation to the inverse and related operators for high-dimensional elliptic problems
• Accurate evaluation of electrostatics for macromolecules in solution
• Low-rank quadrature-based tensor approximation of the Galerkin projected Newton/Yukawa kernels
• Range-separated tensor decomposition of the discretized Dirac delta and elliptic operator inverse
• On preconditioning the treecode-accelerated boundary integral (TABI) Poisson-Boltzmann solver
• An integral equation approach to calculate electrostatic interactions in many-body dielectric systems
• Tensor Numerical Methods in Quantum Chemistry
• Aggregation-Based Algebraic Multigrid for Convection-Diffusion Equations
• Multigrid Accelerated Tensor Approximation of Function Related Multidimensional Arrays
• A Multilinear Singular Value Decomposition
• An Adaptive, Finite Difference Solver for the Nonlinear Poisson-Boltzmann Equation with Applications to Biomolecular Computations
• Range-Separated Tensor Format for Many-Particle Modeling
• Theory of Solutions of Molecules Containing Widely Separated Charges with Special Application to Zwitterions
• The Finite Element Approximation of the Nonlinear Poisson–Boltzmann Equation
• Structured Rank-(r1, . . . , rd) Decomposition of Function-related Tensors in R_D
• Fast solution of the linearized Poisson-Boltzmann equation with nonaffine parametrized boundary conditions using the reduced basis method

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