A High-Order / Low-Order (HOLO) Algorithm with Low-Rank Evolution for Time-Dependent Transport Calculations

2019 ◽  
Author(s):  
R. McClarren ◽  
Z. Peng
Keyword(s):  
High Order ◽  
Time Dependent ◽  
Low Rank ◽  
Dependent Transport ◽  
Low Order

scholarly journals Integrating Semilinear Wave Problems with Time-Dependent Boundary Values Using Arbitrarily High-Order Splitting Methods

Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1113
Author(s):  
Isaías Alonso-Mallo ◽  
Ana M. Portillo
Keyword(s):  
Numerical Experiments ◽  
Splitting Method ◽  
Method Of Lines ◽  
Time Integration ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
High Order ◽  
Time Dependent ◽  
Boundary Values ◽  
Lipschitz Continuous

The initial boundary-value problem associated to a semilinear wave equation with time-dependent boundary values was approximated by using the method of lines. Time integration is achieved by means of an explicit time method obtained from an arbitrarily high-order splitting scheme. We propose a technique to incorporate the boundary values that is more accurate than the one obtained in the standard way, which is clearly seen in the numerical experiments. We prove the consistency and convergence, with the same order of the splitting method, of the full discretization carried out with this technique. Although we performed mathematical analysis under the hypothesis that the source term was Lipschitz-continuous, numerical experiments show that this technique works in more general cases.

scholarly journals High Order Semi-implicit Multistep Methods for Time-Dependent Partial Differential Equations

2021 ◽  
Author(s):  
Giacomo Albi ◽  
Lorenzo Pareschi
Keyword(s):  
Multistep Methods ◽  
General Setting ◽  
Reaction Diffusion ◽  
Strong Stability ◽  
High Order ◽  
Iterative Solvers ◽  
Time Dependent ◽  
Linear Multistep Methods ◽  
Advection Diffusion Equation ◽  
Separation Of Scales

AbstractWe consider the construction of semi-implicit linear multistep methods that can be applied to time-dependent PDEs where the separation of scales in additive form, typically used in implicit-explicit (IMEX) methods, is not possible. As shown in Boscarino et al. (J. Sci. Comput. 68: 975–1001, 2016) for Runge-Kutta methods, these semi-implicit techniques give a great flexibility, and allow, in many cases, the construction of simple linearly implicit schemes with no need of iterative solvers. In this work, we develop a general setting for the construction of high order semi-implicit linear multistep methods and analyze their stability properties for a prototype linear advection-diffusion equation and in the setting of strong stability preserving (SSP) methods. Our findings are demonstrated on several examples, including nonlinear reaction-diffusion and convection-diffusion problems.

scholarly journals Stepwise introduction of model complexity in a generalized master equation approach to time-dependent transport

2012 ◽  
Vol 61 (2-3) ◽  
pp. 305-316 ◽  
Author(s):  
V. Gudmundsson ◽  
O. Jonasson ◽  
Th. Arnold ◽  
C-S. Tang ◽  
H.-S. Goan ◽  
...  
Keyword(s):  
Master Equation ◽  
Time Dependent ◽  
Model Complexity ◽  
Equation Approach ◽  
Master Equation Approach ◽  
Dependent Transport ◽  
Generalized Master Equation

Polynomial Moving Fitting Method for Edge Identification

2011 ◽  
Vol 308-310 ◽  
pp. 2560-2564 ◽  
Author(s):  
Xiang Rong Yuan
Keyword(s):  
Edge Detection ◽  
Curve Fitting ◽  
Polynomial Function ◽  
High Order ◽  
Polynomial Fitting ◽  
Fitting Method ◽  
Order Polynomial ◽  
Better Than ◽  
Low Order

A moving fitting method for edge detection is proposed in this work. Polynomial function is used for the curve fitting of the column of pixels near the edge. Proposed method is compared with polynomial fitting method without sub-segment. The comparison shows that even with low order polynomial, the effects of moving fitting are significantly better than that with high order polynomial fitting without sub-segment.

Robust low-rank tensor reconstruction using high-order t-SVD

2021 ◽  
Vol 30 (06) ◽  
Author(s):  
Wenjin Qin ◽  
Hailin Wang ◽  
Feng Zhang ◽  
Mingwei Dai ◽  
Jianjun Wang
Keyword(s):  
High Order ◽  
Low Rank ◽  
Rank Tensor
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