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388 results on '"Čiegis, Raimondas"'

1. On Properties of Compact 4th order Finite-Difference Schemes for the Variable Coefficient Wave Equation

Author

Zlotnik, Alexander and Čiegis, Raimondas

Subjects
Mathematics - Numerical Analysis, 65M06, 65M12, 65M15, 65N22
Abstract

We consider an initial-boundary value problem for the $n$-dimensional wave equation with the variable sound speed, $n\geq 1$. We construct three-level implicit in time and compact in space (three-point in each space direction) 4th order finite-difference schemes on the uniform rectangular meshes including their one-parameter (for $n=2$) and three-parameter (for $n=3$) families. We also show that some already known methods can be converted into such schemes. In a unified manner, we prove the conditional stability of schemes in the strong and weak energy norms together with the 4th order error estimate under natural conditions on the time step. We also transform an unconditionally stable 4th order two-level scheme suggested for $n=2$ to the three-level form, extend it for any $n\geq 1$ and prove its stability. We also give an example of a compact scheme for non-uniform in space and time rectangular meshes. We suggest simple fast iterative methods based on FFT to implement the schemes. A new effective initial guess to start iterations is given too. We also present promising results of numerical experiments., Comment: 25 pages, 2 figures, 7 tables

Published
2021

2. A compact higher-order finite-difference scheme for the wave equation can be strongly non-dissipative on non-uniform meshes

Author

Zlotnik, Alexander and Čiegis, Raimondas

Subjects
Mathematics - Numerical Analysis, 65M06, 65M12
Abstract

We study necessary conditions for stability of a Numerov-type compact higher-order finite-difference scheme for the 1D homogeneous wave equation in the case of non-uniform spatial meshes. We first show that the uniform in time stability cannot be valid in any spatial norm provided that the complex eigenvalues appear in the associated mesh eigenvalue problem. Moreover, we prove that then the solution norm grows exponentially in time making the scheme strongly non-dissipative and therefore impractical. Numerical results confirm this conclusion. In addition, for some sequences of refining spatial meshes, an excessively strong condition between steps in time and space is necessary (even for the non-uniform in time stability) which is familiar for explicit schemes in the parabolic case., Comment: 6 pages

Published
2020

3. A Three-Level Parallelisation Scheme and Application to the Nelder-Mead Algorithm

Author

Kriauzienė, Rima, Bugajev, Andrej, and Čiegis, Raimondas

Subjects
Computer Science - Distributed, Parallel, and Cluster Computing
Abstract

We consider a three-level parallelisation scheme. The second and third levels define a classical two-level parallelisation scheme and some load balancing algorithm is used to distribute tasks among processes. It is well-known that for many applications the efficiency of parallel algorithms of the second and third level starts to drop down after some critical parallelisation degree is reached. This weakness of the two-level template is addressed by introduction of one additional parallelisation level. As an alternative to the basic solver some new or modified algorithms are considered on this level. The idea of the proposed methodology is to increase the parallelisation degree by using less efficient algorithms in comparison with the basic solver. As an example we investigate two modified Nelder-Mead methods. For the selected application, a few partial differential equations are solved numerically on the second level, and on the third level the parallel Wang's algorithm is used to solve systems of linear equations with tridiagonal matrices. A greedy workload balancing heuristic is proposed, which is oriented to the case of a large number of available processors. The complexity estimates of the computational tasks are model-based, i.e. they use empirical computational data.

Published
2019

4. High order numerical schemes for solving fractional powers of elliptic operators

Author

Ciegis, Raimondas and Vabishchevich, Petr

Subjects
Computer Science - Numerical Analysis, Mathematics - Numerical Analysis, 26A33, 35R11, 65F60, 65M06
Abstract

In many recent applications when new materials and technologies are developed it is important to describe and simulate new nonlinear and nonlocal diffusion transport processes. A general class of such models deals with nonlocal fractional power elliptic operators. In order to solve these problems numerically it is proposed (Petr N. Vabishchevich, Journal of Computational Physics. 2015, Vol. 282, No.1, pp.289--302) to consider equivalent local nonstationary initial value pseudo-parabolic problems. Previously such problems were solved by using the standard implicit backward and symmetrical Euler methods. In this paper we use the one-parameter family of three-level finite difference schemes for solving the initial value problem for the first order nonstationary pseudo-parabolic problem. The fourth-order approximation scheme is developed by selecting the optimal value of the weight parameter. The results of the theoretical analysis are supplemented by results of extensive computational experiments., Comment: 25 pages, 10 figures

Published
2019

6. A 'converse' stability condition is necessary for a compact higher order scheme on non-uniform meshes

Author

Zlotnik, Alexander and Čiegis, Raimondas

Subjects
Mathematics - Numerical Analysis, 65M06, 65M12
Abstract

The stability bounds and error estimates for a compact higher order Numerov-Crank-Nicolson scheme on non-uniform space meshes for the 1D time-dependent Schr\"odinger equation have been recently derived. This analysis has been done in $L^2$ and $H^1$ mesh norms and used the non-standard "converse" condition $h_\omega\leq c_0\tau$, where $h_\omega$ is the mean space step, $\tau$ is the time step and $c_0>0$. Now we prove that such condition is necessary for some families of non-uniform meshes and any space norm. Also numerical results show unacceptably wrong behavior of numerical solutions (their dramatic mass non-conservation) when this condition is violated., Comment: 6 pages, 2 figures, 1 table

Published
2017

13. Stability of the Higher-Order Splitting Methods for the Nonlinear Schrödinger Equation with an Arbitrary Dispersion Operator.

Author

Amiranashvili, Shalva and Čiegis, Raimondas

Subjects
*NONLINEAR Schrodinger equation, *FOUR-wave mixing, *NONLINEAR optics, *FIBER optics
Abstract

The numerical solution of the generalized nonlinear Schrödinger equation by simple splitting methods can be disturbed by so-called spurious instabilities. We analyze these numerical instabilities for an arbitrary splitting method and apply our results to several well-known higher-order splittings. We find that the spurious instabilities can be suppressed to a large extent. However, they never disappear completely if one keeps the integration step above a certain limit and applies what is considered to be a more accurate higher-order method. The latter can be used to make calculations more accurate with the same numerically stable step, but not to make calculations faster with a much larger step. [ABSTRACT FROM AUTHOR]

Published
2024
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15. A Comparison of Accuracy and Efficiency of Parallel Solvers for Fractional Power Diffusion Problems

Author

Čiegis, Raimondas, Starikovičius, Vadimas, Margenov, Svetozar, Kriauzienė, Rima, Hutchison, David, Series Editor, Kanade, Takeo, Series Editor, Kittler, Josef, Series Editor, Kleinberg, Jon M., Series Editor, Mattern, Friedemann, Series Editor, Mitchell, John C., Series Editor, Naor, Moni, Series Editor, Pandu Rangan, C., Series Editor, Steffen, Bernhard, Series Editor, Terzopoulos, Demetri, Series Editor, Tygar, Doug, Series Editor, Weikum, Gerhard, Series Editor, Wyrzykowski, Roman, editor, Dongarra, Jack, editor, Deelman, Ewa, editor, and Karczewski, Konrad, editor

Published
2018
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26. Modeling and Simulations of Beam Stabilization in Edge-Emitting Broad Area Semiconductor Devices

Author

Radziunas, Mindaugas, Čiegis, Raimondas, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Kobsa, Alfred, Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Weikum, Gerhard, Series editor, Wyrzykowski, Roman, editor, Dongarra, Jack, editor, Karczewski, Konrad, editor, and Waśniewski, Jerzy, editor

Published
2014
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27. Parallel Numerical Algorithms for Simulation of Rectangular Waveguides by Using GPU

Author

Čiegis, Raimondas, Bugajev, Andrej, Kancleris, Žilvinas, Šlekas, Gediminas, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Kobsa, Alfred, Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Weikum, Gerhard, Series editor, Wyrzykowski, Roman, editor, Dongarra, Jack, editor, Karczewski, Konrad, editor, and Waśniewski, Jerzy, editor

Published
2014
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28. On Parallelization of the OpenFOAM-Based Solver for the Heat Transfer in Electrical Power Cables

Author

Čiegis, Raimondas, Starikovičius, Vadimas, Bugajev, Andrej, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Kobsa, Alfred, Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Weikum, Gerhard, Series editor, Lopes, Luís, editor, Žilinskas, Julius, editor, Costan, Alexandru, editor, Cascella, Roberto G., editor, Kecskemeti, Gabor, editor, Jeannot, Emmanuel, editor, Cannataro, Mario, editor, Ricci, Laura, editor, Benkner, Siegfried, editor, Petit, Salvador, editor, Scarano, Vittorio, editor, Gracia, José, editor, Hunold, Sascha, editor, Scott, Stephen L., editor, Lankes, Stefan, editor, Lengauer, Christian, editor, Carretero, Jesus, editor, Breitbart, Jens, editor, and Alexander, Michael, editor

Published
2014
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31. A Mathematical Model of the Cardiovascular System

Author

Štikonienė, Olga, Čiegis, Raimondas, Stankus, Albinas, Capasso, Vincenzo, editor, Mattheij, Robert, editor, Neunzert, Helmut, editor, Scherzer, Otmar, editor, Buikis, Andris, editor, Čiegis, Raimondas, editor, and Fitt, Alistair D., editor

Published
2004
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33. Parameters Identification for Wood Drying

Author

Čiegis, Raimondas, Starikovičius, Vadimas, Štikonas, Arturās, Capasso, Vincenzo, editor, Mattheij, Robert, editor, Neunzert, Helmut, editor, Scherzer, Otmar, editor, Buikis, Andris, editor, Čiegis, Raimondas, editor, and Fitt, Alistair D., editor

Published
2004
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35. Parallel Numerical Algorithms for Simulation of Multidimensional Ill-Posed Nonlinear Diffusion-Advection-Reaction Models

Author

Čiegis, Raimondas, Bugajev, Andrej, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Manninen, Pekka, editor, and Öster, Per, editor

Published
2013
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36. Parallel Algorithms for Parabolic Problems on Graphs

Author

Čiegis, Raimondas, Tumanova, Natalija, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Wyrzykowski, Roman, editor, Dongarra, Jack, editor, Karczewski, Konrad, editor, and Waśniewski, Jerzy, editor

Published
2012
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37. Parallel Numerical Solver for Modelling of Electromagnetic Properties of Thin Conductive Layers

Author

Čiegis, Raimondas, Kancleris, Žilvinas, Šlekas, Gediminas, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Wyrzykowski, Roman, editor, Dongarra, Jack, editor, Karczewski, Konrad, editor, and Wasniewski, Jerzy, editor

Published
2010
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39. Implementation of a Black-Box Global Optimization Algorithm with a Parallel Branch and Bound Template

Author

Čiegis, Raimondas, Baravykaitė, Milda, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Kågström, Bo, editor, Elmroth, Erik, editor, Dongarra, Jack, editor, and Waśniewski, Jerzy, editor

Published
2007
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40. Parallel LOD Scheme for 3D Parabolic Problem with Nonlocal Boundary Condition

Author

Čiegis, Raimondas, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Dough, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Nagel, Wolfgang E., editor, Walter, Wolfgang V., editor, and Lehner, Wolfgang, editor

Published
2006
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41. Parallel Tool for Solution of Multiphase Flow Problems

Author

Čiegis, Raimondas, Jakušev, Alexander, Starikovičius, Vadimas, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Sudan, Madhu, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Dough, Series editor, Vardi, Moshe Y., Series editor, Weikum, Gerhard, Series editor, Wyrzykowski, Roman, editor, Dongarra, Jack, editor, Meyer, Norbert, editor, and Waśniewski, Jerzy, editor

Published
2006
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42. Parallel Global Optimization of Foundation Schemes in Civil Engineering

Author

Čiegis, Raimondas, Baravykaitė, Milda, Belevičius, Rimantas, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Dough, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Dongarra, Jack, editor, Madsen, Kaj, editor, and Waśniewski, Jerzy, editor

Published
2006
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