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We analyze and suggest improvements to a recently developed approximate continuum-electrostatic model for proteins. The model, called BIBEE/I (boundary-integral based electrostatics estimation with interpolation), was able to estimate electrostatic solvation free energies to within a mean unsigned error of 4% on a test set of more than 600 proteins¶a significant improvement over previous BIBEE models. In this work, we tested the BIBEE/I model for its capability to predict residue-by-residue interactions...
This paper addresses some results on the development of an approximate method for computing the acoustic field scattered by a three-dimensional penetrable object immersed into an incompressible fluid. The basic idea of the method consists in using on-surface differential operators that locally reproduce the interior propagation phenomenon. This approach leads to integral equation formulations with a reduced computational cost compared to standard integral formulations coupling both the transmitted...
This paper addresses some results on the development of an approximate method
for computing the acoustic field scattered by a three-dimensional penetrable object immersed into an incompressible
fluid. The basic idea of the method consists in using on-surface differential
operators that locally reproduce the interior propagation phenomenon. This approach leads to
integral equation formulations with a reduced computational cost compared to standard integral formulations coupling
both the transmitted...
The paper is a contribution to the complex variable boundary element method, shortly CVBEM. It is focused on Jordan regions having piecewise regular boundaries without cusps. Dini continuous densities whose modulus of continuity satisfies
are considered on these boundaries. Functions satisfying the Hölder condition of order , , belong to them. The statement that any Cauchy-type integral with such a density can be uniformly approximated by a Cauchy-type integral whose density is a piecewise...
An augmented Lagrangian method, based on boundary variational formulations and fixed point method, is designed and analyzed for the Signorini problem of the Laplacian. Using the equivalence between Signorini boundary conditions and a fixed-point problem, we develop a new iterative algorithm that formulates the Signorini problem as a sequence of corresponding variational equations with the Steklov-Poincaré operator. Both theoretical results and numerical experiments show that the method presented...
Object oriented design has proven itself as a powerful tool in the field of scientific computing. Several software packages, libraries and toolkits exist, in particular in the FEM arena that follow this design methodology providing extensible, reusable, and flexible software while staying competitive to traditionally designed point tools in terms of efficiency. However, the common approach to identify classes is to turn data structures and algorithms of traditional implementations into classes such...
Object oriented design has proven itself as a powerful tool in
the field of scientific computing. Several software packages,
libraries and toolkits exist, in particular in the FEM arena
that follow this design methodology providing extensible, reusable,
and flexible software while staying competitive to traditionally
designed point tools in terms of efficiency. However, the common approach to identify classes is to turn data structures and algorithms of traditional implementations into
...
We consider the symmetric FEM-BEM coupling for the numerical solution of a (nonlinear)
interface problem for the 2D Laplacian. We introduce some new a posteriori
error estimators based on the (h − h/2)-error
estimation strategy. In particular, these include the approximation error for the boundary
data, which allows to work with discrete boundary integral operators only. Using the
concept of estimator reduction, we prove that the proposed adaptive...
We consider the symmetric FEM-BEM coupling for the numerical solution of a (nonlinear)
interface problem for the 2D Laplacian. We introduce some new a posteriori
error estimators based on the (h − h/2)-error
estimation strategy. In particular, these include the approximation error for the boundary
data, which allows to work with discrete boundary integral operators only. Using the
concept of estimator reduction, we prove that the proposed adaptive...
We deal with the Galerkin discretization of the boundary integral equations corresponding to problems with the Helmholtz equation in 3D. Our main result is the semi-analytic integration for the bilinear form induced by the hypersingular operator. Such computations have already been proposed for the bilinear forms induced by the single-layer and the double-layer potential operators in the monograph The Fast Solution of Boundary Integral Equations by O. Steinbach and S. Rjasanow and we base our computations...
Convenient for immediate computer implementation equivalents of Green’s functions are obtained for boundary-contact value problems posed for two-dimensional Laplace and Klein-Gordon equations on some regions filled in with piecewise homogeneous isotropic conductive materials. Dirichlet, Neumann and Robin conditions are allowed on the outer boundary of a simply-connected region, while conditions of ideal contact are assumed on interface lines. The objective in this study is to widen the range of...
This paper addresses the derivation of new second-kind Fredholm combined field integral equations for the Krylov iterative
solution of tridimensional acoustic scattering problems by a smooth closed surface. These integral
equations need the introduction of suitable tangential square-root operators to regularize the formulations.
Existence and uniqueness occur for these formulations. They can be interpreted as
generalizations of the well-known Brakhage-Werner [A. Brakhage and P. Werner,
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