Numerical computation of ε-entropy for parabolic equations with analytic solutions

2004 ◽  
Vol 194 (1-2) ◽  
pp. 65-74
Author(s):  
G.J. Lord ◽  
J. Rougemont
Keyword(s):  
Numerical Computation ◽  
Parabolic Equations ◽  
Analytic Solutions

Quasi-analytic solutions of linear parabolic equations

2013 ◽  
Vol 119 (1) ◽  
pp. 115-145 ◽  
Author(s):  
Yakar Kannai ◽  
Roberto C. Raimondo
Keyword(s):  
Parabolic Equations ◽  
Analytic Solutions ◽  
Linear Parabolic Equations

scholarly journals Schwarz waveform relaxation algorithm for heat equations with distributed delay

2016 ◽  
Vol 20 (suppl. 3) ◽  
pp. 659-667
Author(s):  
Shu-Lin Wu
Keyword(s):  
Numerical Computation ◽  
Distributed Delay ◽  
Computation Time ◽  
Analytic Solutions ◽  
Transmission Conditions ◽  
Waveform Relaxation ◽  
Heat Equations ◽  
Relaxation Algorithm ◽  
Schwarz Waveform Relaxation ◽  
The One

Heat equations with distributed delay are a class of mathematic models that has wide applications in many fields. Numerical computation plays an important role in the investigation of these equations, because the analytic solutions of partial differential equations with time delay are usually unavailable. On the other hand, duo to the delay property, numerical computation of these equations is time-consuming. To reduce the computation time, we analyze in this paper the Schwarz waveform relaxation algorithm with Robin transmission conditions. The Robin transmission conditions contain a free parameter, which has a significant effect on the convergence rate of the Schwarz waveform relaxation algorithm. Determining the Robin parameter is therefore one of the top-priority matters for the study of the Schwarz waveform relaxation algorithm. We provide new formula to fix the Robin parameter and we show numerically that the new Robin parameter is more efficient than the one proposed previously in the literature.

scholarly journals A SEMI-ANALYTIC EIGENVALUE EXTENSION TO THE DOPPLER SLAB ANALYTIC BENCHMARK1

2021 ◽  
Vol 247 ◽  
pp. 04018
Author(s):  
Kyle E. Remley ◽  
David P. Griesheimer
Keyword(s):  
Numerical Computation ◽  
Eigenvalue Problems ◽  
Analytic Solutions ◽  
Numerical Implementation ◽  
Numerical Schemes ◽  
Multiphysics Simulation ◽  
Reactivity Coefficient ◽  
Coupled Solvers ◽  
Benchmark Solutions

Advancement in multiphysics simulation has motivated interest in availability of analytic and semi-analytic benchmark solutions. These solutions are sought because they can be used to assess the accuracy of complicated numerical schemes necessary to simulate coupled physics systems. While there exist analytic solutions for fixed-source problems, benchmark-quality eigenvalue solutions are of interest because eigenvalue problems more closely align with analyses undertaken with coupled solvers. This paper extends a fixed-source benchmark, the Doppler Slab benchmark, to the eigenvalue case. A novel solution for this benchmark is derived. Numerical implementation of the benchmark is demonstrated through verification of numerical computation of the power reactivity coefficient.

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