Megala Anandan, Benjamin Boutin, Nicolas Crouseilles
Diffusive scaled linear kinetic equations appear in various applications, and they contain a small parameter $epsilon$ that forces a severe time step restriction for standard explicit schemes. Asymptotic preserving (AP) schemes are those schemes that attain asymptotic consistency and uniform stability for all values of ε, with the time step restriction being independent of ε. In this work, we develop high order AP scheme for such diffusive scaled kinetic equations with both well-prepared and non-well-prepared initial conditions by employing IMEX-RK time integrators such as CK-ARS and A types. This framework is also extended to a different collision model involving advection-diffusion asymptotics, and the AP property is proved formally. A further extension of our framework to inflow boundaries has been made, and the AP property is verified. The temporal and spatial orders of accuracy of our framework are numerically validated in different regimes of ε, for all the models. The qualitative results for diffusion asymptotics, and equilibrium and non-equilibrium inflow boundaries are also presented.
扩散比例线性动力学方程出现在各种应用中，它们包含一个小参数 $epsilon$ ，迫使标准显式方案受到严格的时间步长限制。在这项工作中，我们利用 IMEX-RK 时间积分器（如 CK-ARS 和 A 型），为这种具有良好预处理和非良好预处理初始条件的扩散缩放动力学方程开发了高阶 AP 方案。这一框架还扩展到涉及平流-扩散渐近的不同碰撞模型，并正式证明了 AP 特性。我们还将框架进一步扩展到流入边界，并验证了 AP 特性。对于所有模型，我们框架的时间和空间精度在不同的 ε 条件下都得到了数值验证。还给出了扩散渐近、平衡和非平衡流入边界的定性结果。
{"title":"High order asymptotic preserving scheme for diffusive scaled linear kinetic equations with general initial conditions","authors":"Megala Anandan, Benjamin Boutin, Nicolas Crouseilles","doi":"10.1051/m2an/2024028","DOIUrl":"https://doi.org/10.1051/m2an/2024028","url":null,"abstract":"Diffusive scaled linear kinetic equations appear in various applications, and they contain a small parameter $epsilon$ that forces a severe time step restriction for standard explicit schemes. Asymptotic preserving (AP) schemes are those schemes that attain asymptotic consistency and uniform stability for all values of ε, with the time step restriction being independent of ε. In this work, we develop high order AP scheme for such diffusive scaled kinetic equations with both well-prepared and non-well-prepared initial conditions by employing IMEX-RK time integrators such as CK-ARS and A types. This framework is also extended to a different collision model involving advection-diffusion asymptotics, and the AP property is proved formally. A further extension of our framework to inflow boundaries has been made, and the AP property is verified. The temporal and spatial orders of accuracy of our framework are numerically validated in different regimes of ε, for all the models. The qualitative results for diffusion asymptotics, and equilibrium and non-equilibrium inflow boundaries are also presented.","PeriodicalId":505020,"journal":{"name":"ESAIM: Mathematical Modelling and Numerical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140687855","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A new pipe finite element is proposed for piping analysis within the framework of linear shell theory. The approach involves the use of a mixed interpolation of classical polynomial and trigonometric polynomial spaces, with trigonometric interpolation performed via Hermite-Jackson polynomials along the mid-surface section. Error estimates are provided and a convergence analysis is performed under specific assumptions on the regularity of the solution. The proposed element is validated through several numerical examples, which demonstrate its accuracy and efficiency in terms of computational cost. This method represents a promising approach for addressing the challenges of piping analysis.
{"title":"New pipe element based on Hermite-Jackson interpolation","authors":"E. Zafati, K. Le Nguyen","doi":"10.1051/m2an/2024027","DOIUrl":"https://doi.org/10.1051/m2an/2024027","url":null,"abstract":"A new pipe finite element is proposed for piping analysis within the framework of linear shell theory. The approach involves the use of a mixed interpolation of classical polynomial and trigonometric polynomial spaces, with trigonometric interpolation performed via Hermite-Jackson polynomials along the mid-surface section. Error estimates are provided and a convergence analysis is performed under specific assumptions on the regularity of the solution. The proposed element is validated through several numerical examples, which demonstrate its accuracy and efficiency in terms of computational cost. This method represents a promising approach for addressing the challenges of piping analysis.","PeriodicalId":505020,"journal":{"name":"ESAIM: Mathematical Modelling and Numerical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140709183","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this work, we construct a structure-preserving Galerkin reduced-order model for the resolution of parametric cross-diffusion systems. Cross-diffusion systems are often used to model the evolution of the concentrations or volumic fractions of mixtures composed of different species, and can also be used in population dynamics (as for instance in the SKT system). These systems often read as nonlinear degenerated parabolic partial differential equations, the numerical resolutions of which are highly ex- pensive from a computational point of view. We are interested here in cross-diffusion systems which exhibit a so-called entropic structure, in the sense that they can be formally written as gradient flows of a certain entropy functional which is actually a Lyapunov functional of the system. In this work, we propose a new reduced-order modelling method, based on a reduced basis paradigm, for the resolution of parameter-dependent cross-diffusion systems. Our method preserves, at the level of the reduced-order model, the main mathematical properties of the continuous solution, namely mass conservation, non- negativeness, preservation of the volume-filling property and entropy-entropy dissipation relationship. The theoretical advantages of our approach are illustrated by several numerical experiments.
{"title":"Structure-preserving reduced order model for cross-diffusion systems","authors":"Jad Dabaghi, Virginie Ehrlacher","doi":"10.1051/m2an/2024026","DOIUrl":"https://doi.org/10.1051/m2an/2024026","url":null,"abstract":"In this work, we construct a structure-preserving Galerkin reduced-order model for the resolution\u0000of parametric cross-diffusion systems. Cross-diffusion systems are often used to model the evolution of\u0000the concentrations or volumic fractions of mixtures composed of different species, and can also be used\u0000in population dynamics (as for instance in the SKT system). These systems often read as nonlinear\u0000degenerated parabolic partial differential equations, the numerical resolutions of which are highly ex-\u0000pensive from a computational point of view. We are interested here in cross-diffusion systems which\u0000exhibit a so-called entropic structure, in the sense that they can be formally written as gradient flows\u0000of a certain entropy functional which is actually a Lyapunov functional of the system. In this work, we\u0000propose a new reduced-order modelling method, based on a reduced basis paradigm, for the resolution\u0000of parameter-dependent cross-diffusion systems. Our method preserves, at the level of the reduced-order\u0000model, the main mathematical properties of the continuous solution, namely mass conservation, non-\u0000negativeness, preservation of the volume-filling property and entropy-entropy dissipation relationship.\u0000The theoretical advantages of our approach are illustrated by several numerical experiments.","PeriodicalId":505020,"journal":{"name":"ESAIM: Mathematical Modelling and Numerical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140710085","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the numerical approximation of sign-shifting problems of elliptic type. We fully analyze and assess the method briefly introduced in [Abdulle, Huber, Lemaire; CRAS, 17]. Our method is based on domain decomposition and optimization. Upon an extra integrability assumption on the exact normal flux trace along the sign-changing interface, our method is proved to be convergent as soon as, for a given loading, the PDE admits a unique solution of finite energy. Departing from the T-coercivity approach, which relies on the use of geometrically fitted mesh families, our method works for arbitrary (interface-compliant) mesh sequences. Moreover, it is shown convergent for a class of problems for which T-coercivity is not applicable. A comprehensive set of test-cases complements our analysis.
{"title":"An optimization-based method for sign-changing elliptic PDEs","authors":"A. Abdulle, Simon Lemaire","doi":"10.1051/m2an/2024013","DOIUrl":"https://doi.org/10.1051/m2an/2024013","url":null,"abstract":"We study the numerical approximation of sign-shifting problems of elliptic type. We fully analyze and assess the method briefly introduced in [Abdulle, Huber, Lemaire; CRAS, 17]. Our method is based on domain decomposition and optimization. Upon an extra integrability assumption on the exact normal flux trace along the sign-changing interface, our method is proved to be convergent as soon as, for a given loading, the PDE admits a unique solution of finite energy. Departing from the T-coercivity approach, which relies on the use of geometrically fitted mesh families, our method works for arbitrary (interface-compliant) mesh sequences. Moreover, it is shown convergent for a class of problems for which T-coercivity is not applicable. A comprehensive set of test-cases complements our analysis.","PeriodicalId":505020,"journal":{"name":"ESAIM: Mathematical Modelling and Numerical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140742071","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Maxwell’s equations describe the propagation of electromagnetic waves and are therefore fundamental to understanding many problems encountered in the study of antennas and electromagnetics. The aim of this paper is to propose and analyse an efficient fully discrete scheme for solving three-dimensional Maxwell’s equations. This is accomplished by combining Fourier pseudospectral methods in space and exact formulation in time. Fast computation is efficiently implemented in the scheme by using the matrix diagonalisation method and fast Fourier transform algorithm which are well known in scientific computations. An optimal error estimate which is not encumbered by the CFL condition is established and the resulting scheme is proved to be of spectral accuracy in space and exact in time. Furthermore, the scheme is shown to have multiple conservation laws including discrete energy, helicity, momentum, symplecticity, and divergence-free field conservations. All the theoretical results of the accuracy and conservations are numerically illustrated by two numerical tests.
{"title":"An exact in time Fourier pseudospectral method with multiple conservation laws for three-dimensional Maxwell’s equations","authors":"Bin Wang, Yao-Lin Jiang","doi":"10.1051/m2an/2024022","DOIUrl":"https://doi.org/10.1051/m2an/2024022","url":null,"abstract":"Maxwell’s equations describe the propagation of electromagnetic waves and are therefore fundamental to understanding many problems encountered in the study of antennas and electromagnetics. The aim of this paper is to propose and analyse an efficient fully discrete scheme for solving three-dimensional Maxwell’s equations. This is accomplished by combining Fourier pseudospectral methods in space and exact formulation in time. Fast computation is efficiently implemented in the scheme by using the matrix diagonalisation method and fast Fourier transform algorithm which are well known in scientific computations. An optimal error estimate which is not encumbered by the CFL condition is established and the resulting scheme is proved to be of spectral accuracy in space and exact in time. Furthermore, the scheme is shown to have multiple conservation laws including discrete energy, helicity, momentum, symplecticity, and divergence-free field conservations. All the theoretical results of the accuracy and conservations are numerically illustrated by two numerical tests.","PeriodicalId":505020,"journal":{"name":"ESAIM: Mathematical Modelling and Numerical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140210253","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We propose and analyse the optimized Schwarz waveform relaxation (OSWR) method for the unsteady incompressible Stokes equations. Well-posedness of the local subdomain problems with Robin boundary conditions is proved. Convergence of the velocity is shown through energy estimates; however, pressure converges only up to constant values in the subdomains, and an astute correction technique is proposed to recover these constants from the velocity. The convergence factor of the OSWR algorithm is obtained through a Fourier analysis, and allows to efficiently optimize the space-time Robin transmission conditions involved in the OSWR method. Then, numerical illustrations for the two-dimensional unsteady incompressible Stokes system are presented to illustrate the performance of the OSWR algorithm.
我们提出并分析了针对非稳态不可压缩斯托克斯方程的优化施瓦茨波形松弛（OSWR）方法。我们证明了具有 Robin 边界条件的局部子域问题的良好求解性。通过能量估计显示了速度的收敛性；然而，压力只收敛到子域中的恒定值，并提出了一种精明的修正技术来从速度中恢复这些恒定值。通过傅立叶分析获得了 OSWR 算法的收敛因子，从而可以有效优化 OSWR 方法中涉及的时空罗宾传输条件。然后，给出了二维非稳态不可压缩斯托克斯系统的数值示例，以说明 OSWR 算法的性能。
{"title":"Optimized Schwarz Waveform Relaxation method for the incompressible Stokes problem","authors":"Duc Quang Bui, C. Japhet, P. Omnes","doi":"10.1051/m2an/2024020","DOIUrl":"https://doi.org/10.1051/m2an/2024020","url":null,"abstract":"We propose and analyse the optimized Schwarz waveform relaxation (OSWR) method for the unsteady incompressible Stokes equations. Well-posedness of the local subdomain problems with Robin boundary conditions is proved. Convergence of the velocity is shown through energy estimates; however, pressure converges only up to constant values in the subdomains, and an astute correction technique is proposed to recover these constants from the velocity. The convergence factor of the OSWR algorithm is obtained through a Fourier analysis, and allows to efficiently optimize the space-time Robin transmission conditions involved in the OSWR method. Then, numerical illustrations for the two-dimensional unsteady incompressible Stokes system are presented to illustrate the performance of the OSWR algorithm.","PeriodicalId":505020,"journal":{"name":"ESAIM: Mathematical Modelling and Numerical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140233811","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We prove that there exists a unique solution to the initial value problem describing the motion of a particle subject to a unilateral constraint and Coulomb friction, if the external force acting on the particle is an analytic function of time and of the particle’s position and velocity. Previous work claimed that this problem has a local series solution that corresponds to an analytic function, after any impacts have been resolved. However, a counterexample to that claim was recently discovered, involving a particle starting to slide, in which the series solution is divergent, and thus does not correspond to an analytic function. This paper corrects previous arguments by considering a general formal series solution for a particle that is starting to slide.
{"title":"Existence and uniqueness of the motion of a particle subject to a unilateral constraint and friction","authors":"Christopher Roger Dance","doi":"10.1051/m2an/2024018","DOIUrl":"https://doi.org/10.1051/m2an/2024018","url":null,"abstract":"We prove that there exists a unique solution to the initial value problem describing the motion of a particle subject to a unilateral constraint and Coulomb friction, if the external force acting on the particle is an analytic function of time and of the particle’s position and velocity. Previous work claimed that this problem has a local series solution that corresponds to an analytic function, after any impacts have been resolved. However, a counterexample to that claim was recently discovered, involving a particle starting to slide, in which the series solution is divergent, and thus does not correspond to an analytic function. This paper corrects previous arguments by considering a general formal series solution for a particle that is starting to slide.","PeriodicalId":505020,"journal":{"name":"ESAIM: Mathematical Modelling and Numerical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140250415","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we construct, analyze, and numerically validate a linearized Crank-Nicolson virtual element method (VEM) for solving quasilinear parabolic problems on general polygonal meshes. In particular, we consider the more general nonlinear term a(x,u), which does not require Lipschitz continuity or uniform ellipticity conditions. To ensure that the fully discrete solution remains bounded in L∞ norm, we construct two novel elliptic projections and apply a new error splitting technique. With the help of the boundedness of the numerical solution and delicate analysis of the nonlinear term, we derive the optimal error estimates for any k-order VEMs without any time-step restrictions. Numerical experiments on various polygonal meshes validate the accuracy of the theoretical analysis and the unconditional convergence of the proposed scheme.
{"title":"Unconditionally optimal error estimates of linearized Crank-Nicolson Virtual element methods for quasilinear parabolic problems on general polygonal meshes","authors":"Yang Wang, Huaming Yi, Xiaohong Fan, Guanrong Li","doi":"10.1051/m2an/2024017","DOIUrl":"https://doi.org/10.1051/m2an/2024017","url":null,"abstract":"In this paper, we construct, analyze, and numerically validate a linearized Crank-Nicolson virtual element method (VEM) for solving quasilinear parabolic problems on general polygonal meshes. In particular, we consider the more general nonlinear term a(x,u), which does not require Lipschitz continuity or uniform ellipticity conditions. To ensure that the fully discrete solution remains bounded in L∞ norm, we construct two novel elliptic projections and apply a new error splitting technique. With the help of the boundedness of the numerical solution and delicate analysis of the nonlinear term, we derive the optimal error estimates for any k-order VEMs without any time-step restrictions. Numerical experiments on various polygonal meshes validate the accuracy of the theoretical analysis and the unconditional convergence of the proposed scheme.","PeriodicalId":505020,"journal":{"name":"ESAIM: Mathematical Modelling and Numerical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140254071","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we consider the problem of accelerating the numerical simulation of time dependent problems involving a multi-step time scheme by the parareal algorithm. The parareal method is based on combining predictions made by a coarse and cheap propagator, with corrections computed with two propagators: the previous coarse and a precise and expensive one used in a parallel way over the time windows. A multi-step time scheme can potentially bring higher approximation orders than plain one-step methods but the initialisation of each time window needs to be appropriately chosen. Our main contribution is the design and analysis of an algorithm adapted to this type of discretisation without being too much intrusive in the coarse or fine propagators. At convergence, the parareal algorithm provides a solution that coincides with the solution of the fine solver. In the classical version of parareal, the local initial condition of each time window is corrected at every iteration. When the fine and/or coarse propagators is a multi-step time scheme, we need to choose a consistent approximation of the solutions involved in the initialisation of the fine solver at each time windows. Otherwise, the initialisation error will prevent the parareal algorithm to converge towards the solution with fine solver’s accuracy. In this paper, we develop a variant of the algorithm that overcome this obstacle. Thanks to this, the parareal algorithm is more coherent with the underlying time scheme and we recover the properties of the original version. We show both theoretically and numerically that the accuracy and convergence of the multi-step variant of parareal algorithm are preserved when we choose carefully the initialisation of each time window.
{"title":"Multi-step variant of the parareal algorithm: convergence analysis and numerics","authors":"Katia Ait-Ameur, Y. Maday","doi":"10.1051/m2an/2024014","DOIUrl":"https://doi.org/10.1051/m2an/2024014","url":null,"abstract":"In this paper, we consider the problem of accelerating the numerical simulation of time dependent problems involving a multi-step time scheme by the parareal algorithm. The parareal method is based on combining predictions made by a coarse and cheap propagator, with corrections\u0000computed with two propagators: the previous coarse and a precise and expensive one used in a parallel way over the time windows. A multi-step time scheme can potentially bring higher approximation orders than plain one-step methods but the initialisation of each time window needs to be appropriately chosen. Our main contribution is the design and analysis of an algorithm adapted to this type of discretisation without being too much intrusive in the coarse or fine propagators. At convergence, the parareal algorithm provides a solution that coincides with the solution of the fine solver. In the classical version of parareal, the local initial condition of each time window is corrected at every iteration. When the fine and/or coarse propagators is a multi-step time scheme, we need to choose a consistent approximation of the solutions involved in the initialisation of the fine solver at each time windows. Otherwise, the initialisation error will prevent the parareal algorithm to converge towards the solution with fine solver’s accuracy. In this paper, we develop a variant of the algorithm that overcome this obstacle. Thanks to this, the parareal algorithm is more coherent with the underlying time scheme and we recover the properties of the original version. We show both theoretically and numerically that the accuracy and convergence of the multi-step variant of parareal algorithm are preserved when we choose carefully the initialisation of each time window.","PeriodicalId":505020,"journal":{"name":"ESAIM: Mathematical Modelling and Numerical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140262486","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract. In this paper a technique is given to recover the classical order of the method when explicit exponential Runge-Kutta methods integrate reaction-diffusion problems. In the literature, methods of high enough stiff order for problems with vanishing boundary conditions have been constructed, but that implies restricting the coefficients and thus, the number of stages and the computational cost may significantly increase with respect to other methods without those restrictions. In contrast, the technique which is suggested here is cheaper because it just needs, for any method, to add some terms with information only on the boundaries. Moreover, time-dependent boundary conditions are directly tackled here.
{"title":"Solving reaction-diffusion problems with explicit Runge-Kutta exponential methods without order reduction","authors":"Begoña Cano, María Jesús Moreta","doi":"10.1051/m2an/2024011","DOIUrl":"https://doi.org/10.1051/m2an/2024011","url":null,"abstract":"Abstract. In this paper a technique is given to recover the classical order of the method when explicit exponential Runge-Kutta methods integrate reaction-diffusion problems. In the literature, methods of high enough stiff order for problems with vanishing boundary conditions have been constructed, but that implies restricting the coefficients and thus, the number of stages and the computational cost may significantly increase with respect to other methods without those restrictions. In contrast, the technique which is suggested here is cheaper because it just needs, for any method, to add some terms with information only on the boundaries. Moreover, time-dependent boundary conditions are directly tackled here.","PeriodicalId":505020,"journal":{"name":"ESAIM: Mathematical Modelling and Numerical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139854364","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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