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  • 1
    Electronic Resource
    Electronic Resource
    A rapid method for calculating derivatives of solvent accessible surface areas of molecules (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 16 (1995), S. 1038-1044 
    Details
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: A novel method to calculate the derivatives of solvent accessible surface areas is presented. Unlike earlier analytic methods, which require the molecular topology and the use of global Gauss-Bonnet theorem, this method requires only the fractional accessibilities of surface arcs. We developed an efficient numerical algorithm to calculate the surface arcs by creating a uniform set of points on the circles of intersection between surface atoms. A hierarchical point density doubling scheme led to a logarithmic dependence of Central Processing Unit (CPU) time on the number of points used. This algorithm calculated area derivatives for a 1000-atom protein in 1.5 s on an SGI INDIGO2 which were within 2% of the analytic area derivatives calculated with the program ANAREA. This algorithm scales linearly with the number of atoms for large molecules and is easily parallelizable. © 1995 by John Wiley & Sons, Inc.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jcc.540160810
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    The fast multipole boundary element method for molecular electrostatics: An optimal approach for large systems (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 16 (1995), S. 898-913 
    Details
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: We propose a fast implementation of the boundary element method for solving the Poisson equation, which approximately determines the electrostatic field around solvated molecules of arbitrary shape. The method presented uses computational resources of order O(N) only, where N is the number of elements representing the dielectric boundary at the molecular surface. The method is based on the Fast Multipole Algorithm by Rokhlin and Greengard, which is used to calculate the Coulombic interaction between surface elements in linear time. We calculate the solvation energies of a sphere, a small polar molecule, and a moderately sized protein. The values obtained by the boundary element method agree well with results from finite difference calculations and show a higher degree of consistency due to the absence of grid dependencies. The boundary element method can be taken to a much higher accuracy than is possible with finite difference methods and can therefore be used to verify their validity. © 1995 by John Wiley & Sons, Inc.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jcc.540160707
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    A special incremental-iterative solution technique for non-linear structural analysis including snap-through (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 703-712 
    Details
    ISSN: 1069-8299
    Keywords: non-linear structural analysis ; incremental-iterative solution ; conjugate gradient-like method ; arc length algorithm ; snap-through ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A special incremental-iterative solution method for non-linear finite element structural analysis including snap-through is presented. As an alternative to the direct solution methods, a special iterative strategy along with the pseudoload method is employed within each Newton-Raphson iteration step. Two new developments concerning the pseudoload method and the special iterative strategy, which were originally conceived and applied for the non-linear analysis of shells of revolution using a semi-analytical method, are presented. Firstly, the underlying principles of the method are utilized in solving general non-linear structural mechanics problems. Secondly, the capability of the method is enhanced for tracing the load-displacement curve beyond the critical load by integrating the arc length method. Special modifications are proposed to handle situations with a non-positive-definite tangential stiffness matrix. Numerical examples with snap-through and snap-back phases in the load-deflection path are presented to demonstrate the applicability and accuracy of this approach. Results obtained from this numerical study verify the usefulness of this method as an alternative to the conventional direct methods or iterative methods of solving linearized equations in an incremental non-linear analysis.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640110809
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    Paper (German National Licenses)
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