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DC Field | Value | Language |
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dc.contributor.author | Benner, Peter | - |
dc.contributor.author | Khoromskaia, Venera | - |
dc.contributor.author | Khoromskij, Boris | - |
dc.contributor.author | Stein, Matthias | - |
dc.date.accessioned | 2021-08-17T10:01:52Z | - |
dc.date.available | 2021-08-17T10:01:52Z | - |
dc.date.issued | 2021 | - |
dc.identifier.uri | http://ir.mu.ac.ke:8080/jspui/handle/123456789/5030 | - |
dc.description.abstract | In this paper, we present a new regularization scheme for the linearized Poisson– Boltzmann equation (PBE) which models the electrostatic potential of biomolecules in a solvent. This scheme is based on the splitting of the target potential into the short- and long-range compo- nents localized in the molecular region by using the range-separated (RS) tensor format [P. Benner, V. Khoromskaia, and B. N. Khoromskij, SIAM J. Comput., 2 (2018), pp. A1034–A1062] for represen- tation of the discretized multiparticle Dirac delta [B. N. Khoromskij, J. Comput. Phys., 401 (2020), 108998] constituting the highly singular right-hand side in the PBE. From the computational point of view our regularization approach requires only the modification of the right-hand side in the PBE so that it can be implemented within any open-source grid-based software package for solving PBE that already includes some FEM/FDM disretization scheme for elliptic PDE and solver for the arising lin- ear system of equations. The main computational benefits are twofold. First, one applies the chosen PBE solver only for the smooth long-range (regularized) part of the collective potential with the regu- lar right-hand side represented by a low-rank RS tensor with a controllable precision. Thus, we elimi- nate the numerical treatment of the singularities in the right-hand side and do not change the interface and boundary conditions. And second, the elliptic PDE need not be solved for the singular part in the right-hand side at all, since the short-range part of the target potential of the biomolecule is precom- puted independently on a computational grid by simple one-dimensional tensor operations. The total potential is then obtained by adding the numerical solution of the PBE for the smooth long-range part to the directly precomputed tensor representation for the short-range contribution. Numerical tests illustrate that the new regularization scheme, implemented by a simple modification of the right-hand side in the chosen PBE solver, improves the accuracy of the approximate solution on rather coarse grids. The scheme also demonstrates good convergence behavior on a sequence of refined grids. | en_US |
dc.publisher | Siam | en_US |
dc.subject | Poisson–Boltzmann equation | en_US |
dc.subject | Coulomb potential | en_US |
dc.subject | Summation of electrostatic | en_US |
dc.subject | Potentials | en_US |
dc.subject | long-range many-particle interactions | en_US |
dc.subject | low-rank tensor decompositions | en_US |
dc.subject | Range-separated | en_US |
dc.subject | Tensor formats | en_US |
dc.title | Regularization of poisson–boltzmann type equations with singular source terms using the range-separated tensor format | en_US |
dc.type | Article | en_US |
Appears in Collections: | School of Biological and Physical Sciences |
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benner_3025081.pdf | 1.26 MB | Adobe PDF | View/Open |
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