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An implicit boundary integral method for computing electric potential of macromolecules in solvent. (English) Zbl 1383.78014
Summary: A numerical method using implicit surface representations is proposed to solve the linearized Poisson-Boltzmann equation that arises in mathematical models for the electrostatics of molecules in solvent. The proposed method uses an implicit boundary integral formulation to derive a linear system defined on Cartesian nodes in a narrowband surrounding the closed surface that separates the molecule and the solvent. The needed implicit surface is constructed from the given atomic description of the molecules, by a sequence of standard level set algorithms. A fast multipole method is applied to accelerate the solution of the linear system. A few numerical studies involving some standard test cases are presented and compared to other existing results.

MSC:
78A30 Electro- and magnetostatics
78M15 Boundary element methods applied to problems in optics and electromagnetic theory
78M16 Multipole methods applied to problems in optics and electromagnetic theory
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
92C40 Biochemistry, molecular biology
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