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Vassilevski Y.,Institute of Numerical Mathematics
Engineering with Computers | Year: 2010

In the adaptive mesh generation, the space mesh should be adequate to the surface mesh. When the analytical surface representation is not known, additional surface information may be extracted from triangular surface meshes. We describe a new surface reconstruction method which uses approximate Hessian of a piecewise linear function representing the discrete surface. Efficiency of the proposed method is illustrated with two CFD applications. © Springer-Verlag London Limited 2009. Source


Oseledets I.,Institute of Numerical Mathematics
IEEE Transactions on Computers | Year: 2011

It is well known that Chinese Remainder Theorem (CRT) can be used to construct efficient algorithms for multiplication of polynomials over GF(2). In this note, we show how to select an appropriate set of modulus polynomials to obtain minimal number of multiplications. © 2011 IEEE. Source


Agouzal A.,University of Lyon | Lipnikov K.,Los Alamos National Laboratory | Vassilevski Y.,Institute of Numerical Mathematics
Proceedings of the 20th International Meshing Roundtable, IMR 2011 | Year: 2011

For a given function, we consider a problem of minimizing the P1 interpolation error on a set of triangulations with a fixed number of triangles. The minimization problem is reformulated as a problem of generating a mesh which is quasi-uniform in a specially designed metric. For functions with indefinite Hessian, we show existence of a family of metrics with highly diverse properties. The family may include both anisotropic and isotropic metrics. A developed theory is verified with numerical examples. Source


Achatz U.,Goethe University Frankfurt | Lobl U.,Goethe University Frankfurt | Lobl U.,Institute of Numerical Mathematics | Dolaptchiev S.I.,Goethe University Frankfurt | Gritsun A.,Goethe University Frankfurt
Journal of the Atmospheric Sciences | Year: 2013

Climate-system models use a multitude of parameterization schemes for small-scale processes. These should respond to externally forced climate variability in an appropriate manner so as to reflect the response of the parameterized process to a changing climate. The most attractive route to achieve such a behavior would certainly be provided by theoretical understanding sufficiently deep to enable the a priori design of climate-sensitive parameterization schemes. An alternative path might, however, be helpful when the parameter tuning involved in the development of a scheme is objective enough so that these parameters can be described as functions of the statistics of the climate system. Provided thatthe dynamics of the process in question is sufficiently stochastic, and that the external forcing is not too strong, the fluctuation-dissipation theorem (FDT) might be a tool to predict from the statistics of a system (e.g., the atmosphere) how an objectively tuned parameterization should respond to external forcing (e.g., by anomalous sea surface temperatures). This problem is addressed within the framework of low-order (reduced) models for barotropic flow on the sphere,based on a few optimal basis functions and using an empirical linear subgrid-scale (SGS) closure. A reduced variant of quasi-Gaussian FDT (rqG-FDT) is used to predict the response of the SGS closure to anomalous local vorticity forcing. At sufficiently weak forcing, use of the rqG-FDT is found to systematically improve the agreement between the response of a reduced model and that of a classic spectral code for the solution of the barotropic vorticity equation. © 2013 American Meteorological Society. Source


Litsarev M.S.,Skolkovo Institute of Science and Technology | Oseledets I.V.,Skolkovo Institute of Science and Technology | Oseledets I.V.,Institute of Numerical Mathematics
Computer Physics Communications | Year: 2014

We present a new version of the DEPOSIT computer code based on the low rank approximations. This approach is based on the two dimensional cross decomposition of matrices and separated representations of analytical functions. The cross algorithm is available in the distributed package and can be used independently. All integration routines related to the computation of the deposited energy T (b) are implemented in a new way (low rank separated representation format on homogeneous meshes). By using this approach a bug in integration routines of previous version of the code was found and fixed in the current version. The total computational time was significantly accelerated and is about several minutes. New version program summary: Program title: DEPOSIT 2014. Catalogue identifier: AENP_v2_0. Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AENP_v2_0.html. Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland. Licensing provisions: GNU General Public License, version 3. No. of lines in distributed program, including test data, etc.: 182103. No. of bytes in distributed program, including test data, etc.: 1163484. Distribution format: tar.gz. Programming language: C+ +, Fortran. Computer: Any computer that can run C+ + and Fortran compilers. Operating system: Any operating system with installed compilers mentioned above. Tested on Mac OS X 10.9 and Ubuntu 12.04. Has the code been vectorized or parallelized?: Due to the fast computation in the current implementation only a single-threaded version has been developed. Classification: 2.6, 4.10, 4.11, 19.1. External routines: BLAS, LAPACK and ALGLIB. The last one is included in the distribution. Catalogue identifier of previous version: AENP_v1_0. Journal reference of previous version: Comput. Phys. Comm. 184(2013) 432. Does the new version supersede the previous version?: Yes. Nature of problem:. For a given impact parameter b to calculate the deposited energy T (b) as a 3D integral over a coordinate space, and ionization probabilities Pm (b). For a given energy of the projectile to calculate the total and m-fold electron-loss cross sections using T (b) values on the whole b-mesh. Solution method:. Calculation of the 3D-integral T (b) in all points of the b-mesh based on the low rank separated representations of matrices and tensors. For details, please see Ref. [1]. Reasons for new version:. The computation of the deposited energy T (b) integral is the slowest part of the program and should be done as fast as possible. To accelerate the program a new approach based on the low rank approximations was applied. It made computational scheme more stable and decreased the computational time by a factor of ∼ 103. By means of this approach a bug in the integration routines was found and fixed for a special case of the energy gain. Summary of revisions:. A two dimensional cross decomposition algorithm was developed as an independent module and was integrated with the energy gain Δ E. For the Slater density ρ (r) a separated representation via a sum of Gaussians was implemented. The calculation of three dimensional integrals T (b) was totally rewritten by using quadrature schemes based on the cross decomposition for energy gain and separated representations for Slater density. Details are reported in Ref. [1]. Running time:. For a given energy the total and m-fold cross sections are calculated within about several minutes on a single-core. References: [1] M.S. Litsarev, I.V. Oseledets. Fast computation of the deposited energy integrals with the low-rank approximation technique, Computational Science and Discovery 2014 (submitted); arXiv:1403.4068. © 2014 Elsevier B.V. All rights reserved. Source

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