4 results match your criteria Bit Numerical Mathematics[Journal]

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Computing scattering resonances using perfectly matched layers with frequency dependent scaling functions.

BIT Numer Math 2018 20;58(2):373-395. Epub 2018 Jan 20.

Institut für Analysis und Scientific Computing, TU Wien, Wiedner Hauptstraße 8-10, 1040 Vienna, Austria.

Using perfectly matched layers for the computation of resonances in open systems typically produces artificial or spurious resonances. We analyze the dependency of these artificial resonances with respect to the discretization parameters and the complex scaling function. In particular, we study the differences between a standard frequency independent complex scaling and a frequency dependent one. Read More

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http://dx.doi.org/10.1007/s10543-018-0694-0DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6399748PMC
January 2018

Stochastic discrete Hamiltonian variational integrators.

BIT Numer Math 2018 16;58(4):1009-1048. Epub 2018 Aug 16.

1Mathematics Department, Imperial College London, London, SW7 2AZ UK.

Variational integrators are derived for structure-preserving simulation of stochastic Hamiltonian systems with a certain type of multiplicative noise arising in geometric mechanics. The derivation is based on a stochastic discrete Hamiltonian which approximates a type-II stochastic generating function for the stochastic flow of the Hamiltonian system. The generating function is obtained by introducing an appropriate stochastic action functional and its corresponding variational principle. Read More

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http://dx.doi.org/10.1007/s10543-018-0720-2DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6397621PMC

Practical splitting methods for the adaptive integration of nonlinear evolution equations. Part I: Construction of optimized schemes and pairs of schemes.

BIT Numer Math 2017 28;57(1):55-74. Epub 2016 Jul 28.

3Fakultät für Mathematik, Universität Wien, Oskar-Morgenstern-Platz 1, 1090 Wien, Austria.

We present a number of new contributions to the topic of constructing efficient higher-order splitting methods for the numerical integration of evolution equations. Particular schemes are constructed via setup and solution of polynomial systems for the splitting coefficients. To this end we use and modify a recent approach for generating these systems for a large class of splittings. Read More

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http://dx.doi.org/10.1007/s10543-016-0626-9DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6407747PMC

Using interval unions to solve linear systems of equations with uncertainties.

BIT Numer Math 2017 22;57(3):901-926. Epub 2017 Apr 22.

Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria.

An interval union is a finite set of closed and disjoint intervals. In this paper we introduce the interval union Gauss-Seidel procedure to rigorously enclose the solution set of linear systems with uncertainties given by intervals or interval unions. We also present the interval union midpoint and Gauss-Jordan preconditioners. Read More

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http://dx.doi.org/10.1007/s10543-017-0657-xDOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6399682PMC
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