Some scalar double‐well problems eventually lead to a degenerate convex minimization problem with unique stress. We consider the adaptive conforming and nonconforming finite element methods for the scalar double‐well problem with the reliable a posteriori error analysis. A number of experiments confirm the effective decay rates of the methods.
{"title":"Adaptive finite element methods for scalar double‐well problem","authors":"Bingzhen Li, Dongjie Liu","doi":"10.1002/num.23096","DOIUrl":"https://doi.org/10.1002/num.23096","url":null,"abstract":"Some scalar double‐well problems eventually lead to a degenerate convex minimization problem with unique stress. We consider the adaptive conforming and nonconforming finite element methods for the scalar double‐well problem with the reliable a posteriori error analysis. A number of experiments confirm the effective decay rates of the methods.","PeriodicalId":19443,"journal":{"name":"Numerical Methods for Partial Differential Equations","volume":"276 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140070170","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This article develops an efficient fully discrete scheme for a stochastic strongly damped wave equation (SSDWE) driven by an additive noise and presents its error estimates in the strong sense. We use the truncated spectral expansion of the noise to get an approximate equation and prove its regularity. Then we establish a spatio-temporal discretization of the approximate equation by a finite element method in space and an exponential trapezoidal scheme in time. We prove that the combination can derive higher strong convergence order in time than the use of the piecewise approximation of the noise and the exponential Euler scheme or the implicit Euler scheme in time. Particularly, the temporal strong convergence order of the fully discrete scheme reaches <mjx-container aria-label="5 divided by 4 minus epsilon" ctxtmenu_counter="0" ctxtmenu_oldtabindex="1" jax="CHTML" role="application" sre-explorer- style="font-size: 103%; position: relative;" tabindex="0"><mjx-math aria-hidden="true"><mjx-semantics><mjx-mrow data-semantic-children="5,4" data-semantic-content="3" data-semantic- data-semantic-role="subtraction" data-semantic-speech="5 divided by 4 minus epsilon" data-semantic-type="infixop"><mjx-mrow data-semantic-children="0,2" data-semantic-content="1" data-semantic- data-semantic-parent="6" data-semantic-role="division" data-semantic-type="infixop"><mjx-mn data-semantic-annotation="clearspeak:simple" data-semantic-font="normal" data-semantic- data-semantic-parent="5" data-semantic-role="integer" data-semantic-type="number"><mjx-c></mjx-c></mjx-mn><mjx-mo data-semantic- data-semantic-operator="infixop,/" data-semantic-parent="5" data-semantic-role="division" data-semantic-type="operator" rspace="1" space="1"><mjx-c></mjx-c></mjx-mo><mjx-mn data-semantic-annotation="clearspeak:simple" data-semantic-font="normal" data-semantic- data-semantic-parent="5" data-semantic-role="integer" data-semantic-type="number"><mjx-c></mjx-c></mjx-mn></mjx-mrow><mjx-mo data-semantic- data-semantic-operator="infixop,−" data-semantic-parent="6" data-semantic-role="subtraction" data-semantic-type="operator" rspace="1" style="margin-left: 0.056em;"><mjx-c></mjx-c></mjx-mo><mjx-mi data-semantic-annotation="clearspeak:simple" data-semantic-font="italic" data-semantic- data-semantic-parent="6" data-semantic-role="greekletter" data-semantic-type="identifier"><mjx-c></mjx-c></mjx-mi></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml aria-hidden="true" display="inline" unselectable="on"><math altimg="/cms/asset/246ca0b6-0dc3-49d5-80f8-c979b4835343/num23094-math-0001.png" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow data-semantic-="" data-semantic-children="5,4" data-semantic-content="3" data-semantic-role="subtraction" data-semantic-speech="5 divided by 4 minus epsilon" data-semantic-type="infixop"><mrow data-semantic-="" data-semantic-children="0,2" data-semantic-content="1" data-semantic-parent="6" data-semantic-role="division" data-semantic-type="infixo
{"title":"On strong convergence of a fully discrete scheme for solving stochastic strongly damped wave equations","authors":"Chengqiang Xu, Yibo Wang, Wanrong Cao","doi":"10.1002/num.23094","DOIUrl":"https://doi.org/10.1002/num.23094","url":null,"abstract":"This article develops an efficient fully discrete scheme for a stochastic strongly damped wave equation (SSDWE) driven by an additive noise and presents its error estimates in the strong sense. We use the truncated spectral expansion of the noise to get an approximate equation and prove its regularity. Then we establish a spatio-temporal discretization of the approximate equation by a finite element method in space and an exponential trapezoidal scheme in time. We prove that the combination can derive higher strong convergence order in time than the use of the piecewise approximation of the noise and the exponential Euler scheme or the implicit Euler scheme in time. Particularly, the temporal strong convergence order of the fully discrete scheme reaches <mjx-container aria-label=\"5 divided by 4 minus epsilon\" ctxtmenu_counter=\"0\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" role=\"application\" sre-explorer- style=\"font-size: 103%; position: relative;\" tabindex=\"0\"><mjx-math aria-hidden=\"true\"><mjx-semantics><mjx-mrow data-semantic-children=\"5,4\" data-semantic-content=\"3\" data-semantic- data-semantic-role=\"subtraction\" data-semantic-speech=\"5 divided by 4 minus epsilon\" data-semantic-type=\"infixop\"><mjx-mrow data-semantic-children=\"0,2\" data-semantic-content=\"1\" data-semantic- data-semantic-parent=\"6\" data-semantic-role=\"division\" data-semantic-type=\"infixop\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"integer\" data-semantic-type=\"number\"><mjx-c></mjx-c></mjx-mn><mjx-mo data-semantic- data-semantic-operator=\"infixop,/\" data-semantic-parent=\"5\" data-semantic-role=\"division\" data-semantic-type=\"operator\" rspace=\"1\" space=\"1\"><mjx-c></mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"integer\" data-semantic-type=\"number\"><mjx-c></mjx-c></mjx-mn></mjx-mrow><mjx-mo data-semantic- data-semantic-operator=\"infixop,−\" data-semantic-parent=\"6\" data-semantic-role=\"subtraction\" data-semantic-type=\"operator\" rspace=\"1\" style=\"margin-left: 0.056em;\"><mjx-c></mjx-c></mjx-mo><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"6\" data-semantic-role=\"greekletter\" data-semantic-type=\"identifier\"><mjx-c></mjx-c></mjx-mi></mjx-mrow></mjx-semantics></mjx-math><mjx-assistive-mml aria-hidden=\"true\" display=\"inline\" unselectable=\"on\"><math altimg=\"/cms/asset/246ca0b6-0dc3-49d5-80f8-c979b4835343/num23094-math-0001.png\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow data-semantic-=\"\" data-semantic-children=\"5,4\" data-semantic-content=\"3\" data-semantic-role=\"subtraction\" data-semantic-speech=\"5 divided by 4 minus epsilon\" data-semantic-type=\"infixop\"><mrow data-semantic-=\"\" data-semantic-children=\"0,2\" data-semantic-content=\"1\" data-semantic-parent=\"6\" data-semantic-role=\"division\" data-semantic-type=\"infixo","PeriodicalId":19443,"journal":{"name":"Numerical Methods for Partial Differential Equations","volume":"199 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139948964","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, a second-order time discretizing block-centered finite difference method is introduced to solve the compressible wormhole propagation. The optimal second-order error estimates for the porosity, pressure, velocity, concentration and its flux are established carefully in different discrete norms on non-uniform grids. Then by introducing Lagrange multiplier, a novel bound-preserving scheme for concentration is constructed. Finally, numerical experiments are carried out to demonstrate the correctness of theoretical analysis and capability for simulations of compressible wormhole propagation.
{"title":"A second-order time discretizing block-centered finite difference method for compressible wormhole propagation","authors":"Fei Sun, Xiaoli Li, Hongxing Rui","doi":"10.1002/num.23091","DOIUrl":"https://doi.org/10.1002/num.23091","url":null,"abstract":"In this paper, a second-order time discretizing block-centered finite difference method is introduced to solve the compressible wormhole propagation. The optimal second-order error estimates for the porosity, pressure, velocity, concentration and its flux are established carefully in different discrete norms on non-uniform grids. Then by introducing Lagrange multiplier, a novel bound-preserving scheme for concentration is constructed. Finally, numerical experiments are carried out to demonstrate the correctness of theoretical analysis and capability for simulations of compressible wormhole propagation.","PeriodicalId":19443,"journal":{"name":"Numerical Methods for Partial Differential Equations","volume":"6 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139768163","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Retraction: Nurgabyl DN, Uaissov AB. Asymptotic behavior of the solution of a singularly perturbed general boundary value problem with boundary jumps. Numer Methods Partial Differential Eq. 2021; 37: 2375–2392. https://doi.org/10.1002/num.22719
{"title":"Retraction: Asymptotic behavior of the solution of a singularly perturbed general boundary value problem with boundary jumps","authors":"","doi":"10.1002/num.23089","DOIUrl":"https://doi.org/10.1002/num.23089","url":null,"abstract":"<b>Retraction:</b> Nurgabyl DN, Uaissov AB. Asymptotic behavior of the solution of a singularly perturbed general boundary value problem with boundary jumps. <i>Numer Methods Partial Differential Eq</i>. 2021; 37: 2375–2392. https://doi.org/10.1002/num.22719","PeriodicalId":19443,"journal":{"name":"Numerical Methods for Partial Differential Equations","volume":"5 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140153682","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We develop two totally decoupled, linear and second-order accurate numerical methods that are unconditionally energy stable for solving the Cahn–Hilliard–Darcy equations for two phase flows in porous media or in a Hele-Shaw cell. The implicit-explicit Crank–Nicolson leapfrog method is employed for the discretization of the Cahn–Hiliard equation to obtain linear schemes. Furthermore the artificial compression technique and pressure correction methods are utilized, respectively, so that the Cahn–Hiliard equation and the update of the Darcy pressure can be solved independently. We establish unconditionally long time stability of the schemes. Ample numerical experiments are performed to demonstrate the accuracy and robustness of the numerical methods, including simulations of the Rayleigh–Taylor instability, the Saffman–Taylor instability (fingering phenomenon).
{"title":"Fully decoupled unconditionally stable Crank–Nicolson leapfrog numerical methods for the Cahn–Hilliard–Darcy system","authors":"Yali Gao, Daozhi Han","doi":"10.1002/num.23087","DOIUrl":"https://doi.org/10.1002/num.23087","url":null,"abstract":"We develop two totally decoupled, linear and second-order accurate numerical methods that are unconditionally energy stable for solving the Cahn–Hilliard–Darcy equations for two phase flows in porous media or in a Hele-Shaw cell. The implicit-explicit Crank–Nicolson leapfrog method is employed for the discretization of the Cahn–Hiliard equation to obtain linear schemes. Furthermore the artificial compression technique and pressure correction methods are utilized, respectively, so that the Cahn–Hiliard equation and the update of the Darcy pressure can be solved independently. We establish unconditionally long time stability of the schemes. Ample numerical experiments are performed to demonstrate the accuracy and robustness of the numerical methods, including simulations of the Rayleigh–Taylor instability, the Saffman–Taylor instability (fingering phenomenon).","PeriodicalId":19443,"journal":{"name":"Numerical Methods for Partial Differential Equations","volume":"3 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139657304","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We show that the discrete velocity solution converges at the optimal order when solving the steady state Stokes equations by the - mixed finite element method for on 2D triangular grids or on tetrahedral grids, even in the case the inf-sup condition fails. By a simple -projection of the discrete pressure to the space of continuous polynomials, we show this post-processed pressure solution also converges at the optimal order. Both 2D and 3D numerical tests are presented, verifying the theory.
{"title":"On the convergence of 2D P4+ triangular and 3D P6+ tetrahedral divergence-free finite elements","authors":"Shangyou Zhang","doi":"10.1002/num.23088","DOIUrl":"https://doi.org/10.1002/num.23088","url":null,"abstract":"We show that the discrete velocity solution converges at the optimal order when solving the steady state Stokes equations by the <math altimg=\"urn:x-wiley:num:media:num23088:num23088-math-0003\" display=\"inline\" location=\"graphic/num23088-math-0003.png\" overflow=\"scroll\">\u0000<semantics>\u0000<mrow>\u0000<msub>\u0000<mrow>\u0000<mi>P</mi>\u0000</mrow>\u0000<mrow>\u0000<mi>k</mi>\u0000</mrow>\u0000</msub>\u0000</mrow>\u0000$$ {P}_k $$</annotation>\u0000</semantics></math>-<math altimg=\"urn:x-wiley:num:media:num23088:num23088-math-0004\" display=\"inline\" location=\"graphic/num23088-math-0004.png\" overflow=\"scroll\">\u0000<semantics>\u0000<mrow>\u0000<msubsup>\u0000<mrow>\u0000<mi>P</mi>\u0000</mrow>\u0000<mrow>\u0000<mi>k</mi>\u0000<mo form=\"prefix\">−</mo>\u0000<mn>1</mn>\u0000</mrow>\u0000<mrow>\u0000<mtext>disc</mtext>\u0000</mrow>\u0000</msubsup>\u0000</mrow>\u0000$$ {P}_{k-1}^{mathrm{disc}} $$</annotation>\u0000</semantics></math> mixed finite element method for <math altimg=\"urn:x-wiley:num:media:num23088:num23088-math-0005\" display=\"inline\" location=\"graphic/num23088-math-0005.png\" overflow=\"scroll\">\u0000<semantics>\u0000<mrow>\u0000<mi>k</mi>\u0000<mo>≥</mo>\u0000<mn>4</mn>\u0000</mrow>\u0000$$ kge 4 $$</annotation>\u0000</semantics></math> on 2D triangular grids or <math altimg=\"urn:x-wiley:num:media:num23088:num23088-math-0006\" display=\"inline\" location=\"graphic/num23088-math-0006.png\" overflow=\"scroll\">\u0000<semantics>\u0000<mrow>\u0000<mi>k</mi>\u0000<mo>≥</mo>\u0000<mn>6</mn>\u0000</mrow>\u0000$$ kge 6 $$</annotation>\u0000</semantics></math> on tetrahedral grids, even in the case the inf-sup condition fails. By a simple <math altimg=\"urn:x-wiley:num:media:num23088:num23088-math-0007\" display=\"inline\" location=\"graphic/num23088-math-0007.png\" overflow=\"scroll\">\u0000<semantics>\u0000<mrow>\u0000<msup>\u0000<mrow>\u0000<mi>L</mi>\u0000</mrow>\u0000<mrow>\u0000<mn>2</mn>\u0000</mrow>\u0000</msup>\u0000</mrow>\u0000$$ {L}^2 $$</annotation>\u0000</semantics></math>-projection of the discrete <math altimg=\"urn:x-wiley:num:media:num23088:num23088-math-0008\" display=\"inline\" location=\"graphic/num23088-math-0008.png\" overflow=\"scroll\">\u0000<semantics>\u0000<mrow>\u0000<msub>\u0000<mrow>\u0000<mi>P</mi>\u0000</mrow>\u0000<mrow>\u0000<mi>k</mi>\u0000<mo form=\"prefix\">−</mo>\u0000<mn>1</mn>\u0000</mrow>\u0000</msub>\u0000</mrow>\u0000$$ {P}_{k-1} $$</annotation>\u0000</semantics></math> pressure to the space of continuous <math altimg=\"urn:x-wiley:num:media:num23088:num23088-math-0009\" display=\"inline\" location=\"graphic/num23088-math-0009.png\" overflow=\"scroll\">\u0000<semantics>\u0000<mrow>\u0000<msub>\u0000<mrow>\u0000<mi>P</mi>\u0000</mrow>\u0000<mrow>\u0000<mi>k</mi>\u0000<mo form=\"prefix\">−</mo>\u0000<mn>1</mn>\u0000</mrow>\u0000</msub>\u0000</mrow>\u0000$$ {P}_{k-1} $$</annotation>\u0000</semantics></math> polynomials, we show this post-processed pressure solution also converges at the optimal order. Both 2D and 3D numerical tests are presented, verifying the theory.","PeriodicalId":19443,"journal":{"name":"Numerical Methods for Partial Differential Equations","volume":"65 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139560032","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The present study explores the nanofluid boundary layer flow over a stretching sheet with the combined influence of the double diffusive effects of thermophoresis and Brownian motion effects. For the purpose of transforming nonlinear partial differential equations into the linear united ordinary differential equation method, the similarity transformation technique is used. The Runge–Kutta–Fehlberg method was used to solve the equations of flow, along with sufficient boundary conditions. The effect on hydrodynamic, thermal and solutes boundary layers of a number of related parameters is investigated and the effects are graphically displayed. In conclusion, a strong agreement between the current numerical findings and the previous literature results is sought.
{"title":"Double diffusive effects on nanofluid flow toward a permeable stretching surface in presence of Thermophoresis and Brownian motion effects: A numerical study","authors":"V. V. L. Deepthi, V. K. Narla, R. Srinivasa Raju","doi":"10.1002/num.23086","DOIUrl":"https://doi.org/10.1002/num.23086","url":null,"abstract":"The present study explores the nanofluid boundary layer flow over a stretching sheet with the combined influence of the double diffusive effects of thermophoresis and Brownian motion effects. For the purpose of transforming nonlinear partial differential equations into the linear united ordinary differential equation method, the similarity transformation technique is used. The Runge–Kutta–Fehlberg method was used to solve the equations of flow, along with sufficient boundary conditions. The effect on hydrodynamic, thermal and solutes boundary layers of a number of related parameters is investigated and the effects are graphically displayed. In conclusion, a strong agreement between the current numerical findings and the previous literature results is sought.","PeriodicalId":19443,"journal":{"name":"Numerical Methods for Partial Differential Equations","volume":"22 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139499728","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ruben Caraballo, Chansophea Wathanak In, Alberto F. Martín, Ricardo Ruiz-Baier
In this article, we propose a new formulation and a suitable finite element method for the steady coupling of viscous flow in deformable porous media using divergence-conforming filtration fluxes. The proposed method is based on the use of parameter-weighted spaces, which allows for a more accurate and robust analysis of the continuous and discrete problems. Furthermore, we conduct a solvability analysis of the proposed method and derive optimal error estimates in appropriate norms. These error estimates are shown to be robust in a variety of regimes, including the case of large Lamé parameters and small permeability and storativity coefficients. To illustrate the effectiveness of the proposed method, we provide a few representative numerical examples, including convergence verification and testing of robustness of block-diagonal preconditioners with respect to model parameters.
{"title":"Robust finite element methods and solvers for the Biot–Brinkman equations in vorticity form","authors":"Ruben Caraballo, Chansophea Wathanak In, Alberto F. Martín, Ricardo Ruiz-Baier","doi":"10.1002/num.23083","DOIUrl":"https://doi.org/10.1002/num.23083","url":null,"abstract":"In this article, we propose a new formulation and a suitable finite element method for the steady coupling of viscous flow in deformable porous media using divergence-conforming filtration fluxes. The proposed method is based on the use of parameter-weighted spaces, which allows for a more accurate and robust analysis of the continuous and discrete problems. Furthermore, we conduct a solvability analysis of the proposed method and derive optimal error estimates in appropriate norms. These error estimates are shown to be robust in a variety of regimes, including the case of large Lamé parameters and small permeability and storativity coefficients. To illustrate the effectiveness of the proposed method, we provide a few representative numerical examples, including convergence verification and testing of robustness of block-diagonal preconditioners with respect to model parameters.","PeriodicalId":19443,"journal":{"name":"Numerical Methods for Partial Differential Equations","volume":"28 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2023-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138532565","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This article focuses on designing efficient iteration algorithms for nonequilibrium three-temperature heat conduction equations, which are used to formulate the radiative energy transport problem. Based on the framework of relaxation iteration, we design a new accelerated iteration algorithm by reasonable approximation of the Jacobi matrix, according to the characteristics of the discrete scheme for the three-temperature equations. Adopting the iteration framework, we analyze the advantages and disadvantages of several iteration algorithms commonly used in practice and the new iteration algorithm. Finally, we compare the new iteration algorithm with some other iteration algorithms by solving several nonlinear models, and show that the new algorithm can achieve significant acceleration effect.
{"title":"Iteration acceleration methods for solving three-temperature heat conduction equations on distorted meshes","authors":"Yunlong Yu, Xingding Chen, Yanzhong Yao","doi":"10.1002/num.23085","DOIUrl":"https://doi.org/10.1002/num.23085","url":null,"abstract":"This article focuses on designing efficient iteration algorithms for nonequilibrium three-temperature heat conduction equations, which are used to formulate the radiative energy transport problem. Based on the framework of relaxation iteration, we design a new accelerated iteration algorithm by reasonable approximation of the Jacobi matrix, according to the characteristics of the discrete scheme for the three-temperature equations. Adopting the iteration framework, we analyze the advantages and disadvantages of several iteration algorithms commonly used in practice and the new iteration algorithm. Finally, we compare the new iteration algorithm with some other iteration algorithms by solving several nonlinear models, and show that the new algorithm can achieve significant acceleration effect.","PeriodicalId":19443,"journal":{"name":"Numerical Methods for Partial Differential Equations","volume":"3 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2023-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138532564","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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