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Multigrid waveform relaxation for the time-fractional heat equation [article]

Francisco J. Gaspar, Carmen Rodrigo
2017 arXiv   pre-print
In this work, we propose an efficient and robust multigrid method for solving the time-fractional heat equation.  ...  We develop a parallel-in-time multigrid algorithm based on the waveform relaxation approach, whose application to time-fractional problems seems very natural due to the fact that the fractional derivative  ...  Acknowledgments The authors thank the referees for their valuable comments and suggestions which helped to improve the paper.  ... 
arXiv:1608.05400v2 fatcat:sj527ptgozftdam5s6g46sgvb4

Multigrid Waveform Relaxation for the Time-Fractional Heat Equation

Francisco J. Gaspar, Carmen Rodrigo
2017 SIAM Journal on Scientific Computing  
In this work, we propose an efficient and robust multigrid method for solving the time-fractional heat equation.  ...  Our main contribution is to propose an efficient and robust multigrid method based on the waveform relaxation approach to solve the time-fractional heat equation.  ...  The authors thank the referees for their valuable comments and suggestions, which helped to improve the paper.  ... 
doi:10.1137/16m1090193 fatcat:knckcp6xr5fcfa373os7seduyu

Using hierarchical matrices in the solution of the time-fractional heat equation by multigrid waveform relaxation [article]

Xiaozhe Hu, Carmen Rodrigo, Francisco J. Gaspar
2020 arXiv   pre-print
We propose an efficient space-time multigrid method based on the waveform relaxation technique, which accounts for the nonlocal character of the fractional differential operator.  ...  This work deals with the efficient numerical solution of the time-fractional heat equation discretized on non-uniform temporal meshes.  ...  A very satisfactory convergence is observed in all cases, making the multigrid waveform relaxation method a good choice for an efficient solution of the time-fractional two-dimensional heat equation.  ... 
arXiv:1706.07632v3 fatcat:y4pdytyisje3fo5qalihgfbl3i

On Dynamic Iteration Methods for Solving Time-Periodic Differential Equations

Stefan Vandewalle, Robert Piessens
1993 SIAM Journal on Numerical Analysis  
Dynamic iteration or, more popularly, waveform relaxation has received a great deal of attention as an efficient parallel method for solving large systems of ordinary differential equations of initial  ...  In this paper the applicability of the method is further extended to incorporate the class of time-periodic ordinary and partial differential equations.  ...  Time-periodic multigrid dynamic iteration. In [4] a multigrid acceleration for the initial value dynamic iteration was proposed and theoretically analyzed.  ... 
doi:10.1137/0730014 fatcat:ab6tz3jdu5eujn7mbl36zfhfky

subject index volumes 201 to 210

2007 Journal of Computational and Applied Mathematics  
203 362 Heat equation 208 391; 210 183 Heat radiation 203 362 Heat source 209 66 Heat transfer 207 24 Helmholtz decomposition 204 440 Helmholtz equation 203 15; 204 282, 344 Helmholtz problems  ...  206 209 The minimum norm for quadratic programs 206 288 The weighted Chebyshev norm 206 278 Theorem of Lancret 206 116 Theoretical computer science 204 38 Thermo-elastostatics 206 774 Third order iterative  ... 
doi:10.1016/s0377-0427(07)00502-x fatcat:tovvilkoczetvl423gcjxug7gm

Performance and stability of near-unity aspect ratio plasmas in the Pegasus Toroidal Experiment

G. D. Garstka, S. J. Diem, R. J. Fonck, B. T. Lewicki, A. C. Sontag, K. L. Tritz, E. A. Unterberg
2003 Physics of Plasmas  
It has the dual roles of exploring the limits of spherical torus plasma behavior as the aspect ratio, A, approaches 1 and examining alternate confinement concepts in the tokamak-spheromak overlap regime  ...  The Pegasus Toroidal Experiment [1] is a mid-sized, extremely low aspect ratio spherical torus.  ...  Acknowledgement This work is supported by the United States Department of Energy Grant number DE-FG02-96ER54375.  ... 
doi:10.1063/1.1559972 fatcat:7xtqtbupgvejvacq44is3flk6q

A parallel-in-time algorithm for high-order BDF methods for diffusion and subdiffusion equations [article]

Shuonan Wu, Zhi Zhou
2021 arXiv   pre-print
In this paper, we propose a parallel-in-time algorithm for approximately solving parabolic equations.  ...  The argument could be further applied to the time-fractional subdiffusion equation, whose discretization shares common properties of the standard BDF methods, because of the nonlocality of the fractional  ...  The research of S. Wu is partially supported by the National Natural Science Foundation of China grant (No. 11901016) and the startup grant from Peking University. The research of Z.  ... 
arXiv:2007.13125v2 fatcat:chry5yt2rfdczhtob5yl7xljeq

Convergent iterative schemes for time parallelization

Izaskun Garrido, Barry Lee, Gunnar E. Fladmark, Magne S. Espedal
2006 Mathematics of Computation  
But for many evolutionary problems, computer simulation can benefit substantially from time parallelization methods.  ...  Parallel methods are usually not applied to the time domain because of the inherit sequentialness of time evolution.  ...  Two other parallel approaches for time-dependent problems are waveform relaxation and overlapping Schwarz waveform relaxation. These methods do achieve parallelism in time.  ... 
doi:10.1090/s0025-5718-06-01832-1 fatcat:scpukglfwrfbdn5co4bzfk3adu

Krylov Subspace Acceleration of Waveform Relaxation

Andrew Lumsdaine, Deyun Wu
2003 SIAM Journal on Numerical Analysis  
In this paper we describe and analyze Krylov subspace techniques for accelerating the convergence of waveform relaxation for solving time-dependent problems.  ...  Previous approaches for accelerating the convergence of waveform relaxation include the shifted Picard iteration [34], multigrid [18, 41], SOR [23], Chebyshev acceleration [17], convolution SOR [30], L  ...  Convolution Krylov subspace algorithms have tantalized the authors for several years.  ... 
doi:10.1137/s0036142996313142 fatcat:ot47ra4s3vh4ripcudvedm3mdm

Asymptotic Analysis for Overlap in Waveform Relaxation Methods for RC Type Circuits [article]

Martin J. Gander, Pratik M. Kumbhar, Albert E. Ruehli
2020 arXiv   pre-print
Waveform relaxation (WR) methods are based on partitioning large circuits into sub-circuits which then are solved separately for multiple time steps in so-called time windows, and an iteration is used  ...  We study here for the first time the influence of overlapping sub-circuits in both WR and OWR applied to RC circuits.  ...  We also showed that our optimized parameters can be used when solving heat equations with waveform relaxation techniques.  ... 
arXiv:2001.04949v1 fatcat:j4dz5opm4je37jzjgbydrpoc4e

Bridging the scales in nano engineering and science

Jacob Fish
2006 Journal of nanoparticle research  
In the concurrent multiscale methods both, the discrete and continuum scales are simultaneously resolved, whereas in the information-passing schemes, the discrete scale is modelled and its gross response  ...  is infused into the continuum scale.  ...  The author wishes to thank Eliot Fang, Harold Park, Roger Ghanem, Ken Chong and Min Zhou for valuable input provided in writing the review article.  ... 
doi:10.1007/s11051-006-9090-9 fatcat:v7yqnwy3ejfaflo2u2iwcewstu

Master index to volumes 31–40

1992 Journal of Computational and Applied Mathematics  
;; XXI Gauss-Lobatro quadratures with double end points Gear, C.W., Waveform methods for space and time pdrallelrsm Geng, P,, see Demkowicz, L.  ...  Iso, Y. and Onishi, K., On the stabthty of the boundary element collocatron method apphed to the linear heat equation Iyengar, S.R.K. and Goyal, A., A note on multrgrrd for the three-dimensional Porsson  ...  ., The double exponential formula for oscdlatory functions over the half mfmlte interval Oyada, N., Accelerable subsets of logarnthmlc sequences Osada, N., Acceleratmn methods for vector sequences <)yanagi  ... 
doi:10.1016/0377-0427(92)90272-y fatcat:d4bhxu5bzvdlxplp45yih4ut2e

Performance of Combination Drug and Hygroscopic Excipient Submicrometer Particles from a Softmist Inhaler in a Characteristic Model of the Airways

P. Worth Longest, Geng Tian, Xiang Li, Yoen-Ju Son, Michael Hindle
2012 Annals of Biomedical Engineering  
Transient inhalation was found to influence the final size of the aerosol based on changes in residence times and relative humidity values.  ...  Aerosol sizes following EEG when exiting the chamber (2.75-4.61 μm) for all cases of initial submicrometer combination particles were equivalent to or larger than many conventional pharmaceutical aerosols  ...  The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Heart, Lung, And Blood Institute or the National Institutes of Health.  ... 
doi:10.1007/s10439-012-0616-2 pmid:22820981 pmcid:PMC3504134 fatcat:c2za52brhbet7css65hbzoxpge

Mergers of irrotational neutron star binaries in conformally flat gravity

Joshua A. Faber, Philippe Grandclément, Frederic A. Rasio
2004 Physical Review D  
In particular, we find that mass loss is highly suppressed by relativistic effects, but that, for a reasonably stiff neutron star equation of state, the remnant is initially stable against gravitational  ...  The code was tested on models for which the CF limit is exact, finding good agreement with the classical Oppenheimer-Volkov solution for a relativistic static spherical star as well as the exact semi-analytic  ...  Last, we took the nonequilibrium configuration from run OV2, but added a ''relaxation'' drag term of the form Ϫũ i /t relax to the RHS of the force equation, Eq. ͑9͒, with t relax /M 0 ϭ7.9.  ... 
doi:10.1103/physrevd.69.124036 fatcat:mjao26aucnhgfnp2vpsq5hwtmu

Scalable Approach to Uncertainty Quantification and Robust Design of Interconnected Dynamical Systems [article]

Andrzej Banaszuk, Vladimir A. Fonoberov, Thomas A. Frewen, Marin Kobilarov, George Mathew, Igor Mezic, Alessandro Pinto, Tuhin Sahai, Harshad Sane, Alberto Speranzon, Amit Surana
2011 arXiv   pre-print
of the problem.  ...  Model-based robust design is difficult because of the complexity of the hybrid dynamic models including continuous vehicle dynamics, the discrete models of computations and communications, and the size  ...  We called the positive influence of the discussions with Jerry Marsden that stayed with us for a long time after the discussions and kept us pursuing the research with hope and excitement "the Jerry effect  ... 
arXiv:1103.0733v1 fatcat:k3tpcelfcrfw7euwzm2ignq2gu
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