Communications on Applied Mathematics and Computation最新文献_第3页

Numerical Approach for Solving Two-Dimensional Time-Fractional Fisher Equation via HABC-N Method 用HABC-N方法求解二维时间分数Fisher方程的数值方法

4区数学

Communications on Applied Mathematics and Computation Pub Date : 2023-09-15 DOI: 10.1007/s42967-023-00282-w

Ren Liu, Lifei Wu

引用次数: 0

A New Efficient Explicit Deferred Correction Framework: Analysis and Applications to Hyperbolic PDEs and Adaptivity 一种新的高效显式延迟校正框架:双曲偏微分方程和自适应的分析与应用

4区数学

Communications on Applied Mathematics and Computation Pub Date : 2023-09-12 DOI: 10.1007/s42967-023-00294-6

Lorenzo Micalizzi, Davide Torlo

引用次数: 0

Efficient Iterative Arbitrary High-Order Methods: an Adaptive Bridge Between Low and High Order 高效迭代任意高阶方法:低阶与高阶之间的自适应桥梁

4区数学

Communications on Applied Mathematics and Computation Pub Date : 2023-09-11 DOI: 10.1007/s42967-023-00290-w

Lorenzo Micalizzi, Davide Torlo, Walter Boscheri

{"title":"Efficient Iterative Arbitrary High-Order Methods: an Adaptive Bridge Between Low and High Order","authors":"Lorenzo Micalizzi, Davide Torlo, Walter Boscheri","doi":"10.1007/s42967-023-00290-w","DOIUrl":"https://doi.org/10.1007/s42967-023-00290-w","url":null,"abstract":"Abstract We propose a new paradigm for designing efficient p -adaptive arbitrary high-order methods. We consider arbitrary high-order iterative schemes that gain one order of accuracy at each iteration and we modify them to match the accuracy achieved in a specific iteration with the discretization accuracy of the same iteration. Apart from the computational advantage, the newly modified methods allow to naturally perform the p -adaptivity, stopping the iterations when appropriate conditions are met. Moreover, the modification is very easy to be included in an existing implementation of an arbitrary high-order iterative scheme and it does not ruin the possibility of parallelization, if this was achievable by the original method. An application to the Arbitrary DERivative (ADER) method for hyperbolic Partial Differential Equations (PDEs) is presented here. We explain how such a framework can be interpreted as an arbitrary high-order iterative scheme, by recasting it as a Deferred Correction (DeC) method, and how to easily modify it to obtain a more efficient formulation, in which a local a posteriori limiter can be naturally integrated leading to the p -adaptivity and structure-preserving properties. Finally, the novel approach is extensively tested against classical benchmarks for compressible gas dynamics to show the robustness and the computational efficiency.","PeriodicalId":29916,"journal":{"name":"Communications on Applied Mathematics and Computation","volume":"66 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135935274","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Hyperbolic Conservation Laws, Integral Balance Laws and Regularity of Fluxes 双曲守恒定律、积分平衡定律和通量的规律性

IF 1.6 4区数学

Communications on Applied Mathematics and Computation Pub Date : 2023-09-04 DOI: 10.1007/s42967-023-00298-2

M. Ben-Artzi, Jiequan Li

引用次数: 0

On the Stability of IMEX Upwind gSBP Schemes for 1D Linear Advection-Diffusion Equations 一维线性平流扩散方程IMEX迎风gSBP格式的稳定性

4区数学

Communications on Applied Mathematics and Computation Pub Date : 2023-08-29 DOI: 10.1007/s42967-023-00296-4

Sigrun Ortleb

{"title":"On the Stability of IMEX Upwind gSBP Schemes for 1D Linear Advection-Diffusion Equations","authors":"Sigrun Ortleb","doi":"10.1007/s42967-023-00296-4","DOIUrl":"https://doi.org/10.1007/s42967-023-00296-4","url":null,"abstract":"Abstract A fully discrete energy stability analysis is carried out for linear advection-diffusion problems discretized by generalized upwind summation-by-parts (upwind gSBP) schemes in space and implicit-explicit Runge-Kutta (IMEX-RK) schemes in time. Hereby, advection terms are discretized explicitly, while diffusion terms are solved implicitly. In this context, specific combinations of space and time discretizations enjoy enhanced stability properties. In fact, if the first- and second-derivative upwind gSBP operators fulfill a compatibility condition, the allowable time step size is independent of grid refinement, although the advective terms are discretized explicitly. In one space dimension it is shown that upwind gSBP schemes represent a general framework including standard discontinuous Galerkin (DG) schemes on a global level. While previous work for DG schemes has demonstrated that the combination of upwind advection fluxes and the central-type first Bassi-Rebay (BR1) scheme for diffusion does not allow for grid-independent stable time steps, the current work shows that central advection fluxes are compatible with BR1 regarding enhanced stability of IMEX time stepping. Furthermore, unlike previous discrete energy stability investigations for DG schemes, the present analysis is based on the discrete energy provided by the corresponding SBP norm matrix and yields time step restrictions independent of the discretization order in space, since no finite-element-type inverse constants are involved. Numerical experiments are provided confirming these theoretical findings.","PeriodicalId":29916,"journal":{"name":"Communications on Applied Mathematics and Computation","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136248387","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Meta-Auto-Decoder: a Meta-Learning-Based Reduced Order Model for Solving Parametric Partial Differential Equations 元自动解码器:一种求解参数偏微分方程的元学习降阶模型

4区数学

Communications on Applied Mathematics and Computation Pub Date : 2023-08-14 DOI: 10.1007/s42967-023-00293-7

Zhanhong Ye, Xiang Huang, Hongsheng Liu, Bin Dong

{"title":"Meta-Auto-Decoder: a Meta-Learning-Based Reduced Order Model for Solving Parametric Partial Differential Equations","authors":"Zhanhong Ye, Xiang Huang, Hongsheng Liu, Bin Dong","doi":"10.1007/s42967-023-00293-7","DOIUrl":"https://doi.org/10.1007/s42967-023-00293-7","url":null,"abstract":"Many important problems in science and engineering require solving the so-called parametric partial differential equations (PDEs), i.e., PDEs with different physical parameters, boundary conditions, shapes of computational domains, etc. Typical reduced order modeling techniques accelerate the solution of the parametric PDEs by projecting them onto a linear trial manifold constructed in the offline stage. These methods often need a predefined mesh as well as a series of precomputed solution snapshots, and may struggle to balance between the efficiency and accuracy due to the limitation of the linear ansatz. Utilizing the nonlinear representation of neural networks (NNs), we propose the Meta-Auto-Decoder (MAD) to construct a nonlinear trial manifold, whose best possible performance is measured theoretically by the decoder width. Based on the meta-learning concept, the trial manifold can be learned in a mesh-free and unsupervised way during the pre-training stage. Fast adaptation to new (possibly heterogeneous) PDE parameters is enabled by searching on this trial manifold, and optionally fine-tuning the trial manifold at the same time. Extensive numerical experiments show that the MAD method exhibits a faster convergence speed without losing the accuracy than other deep learning-based methods.","PeriodicalId":29916,"journal":{"name":"Communications on Applied Mathematics and Computation","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135214939","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A Two-Step Modulus-Based Matrix Splitting Iteration Method Without Auxiliary Variables for Solving Vertical Linear Complementarity Problems 求解垂直线性互补问题的无辅助变量两步模矩阵分裂迭代法

IF 1.6 4区数学

Communications on Applied Mathematics and Computation Pub Date : 2023-08-11 DOI: 10.1007/s42967-023-00280-y

Hua Zheng, Xiaoping Lu, Seakweng Vong

引用次数: 0

An Improved Coupled Level Set and Continuous Moment-of-Fluid Method for Simulating Multiphase Flows with Phase Change 一种改进的耦合水平集和连续流体矩法模拟相变多相流

IF 1.6 4区数学

Communications on Applied Mathematics and Computation Pub Date : 2023-08-11 DOI: 10.1007/s42967-023-00286-6

Zhouteng Ye, Cody Estebe, Yang Liu, M. Vahab, Zeyu Huang, M. Sussman, Alireza Moradikazerouni, K. Shoele, Y. Lian, M. Ohta, M. Hussaini

引用次数: 0

Second-Order Accurate Structure-Preserving Scheme for Solute Transport on Polygonal Meshes 多边形网格上溶质输运的二阶精确保结构格式

IF 1.6 4区数学

Communications on Applied Mathematics and Computation Pub Date : 2023-08-10 DOI: 10.1007/s42967-023-00289-3

Naren Vohra, K. Lipnikov, S. Tokareva

引用次数: 0

An Arbitrarily High Order and Asymptotic Preserving Kinetic Scheme in Compressible Fluid Dynamic 可压缩流体动力学中的任意高阶渐近保持动力学格式

4区数学

Communications on Applied Mathematics and Computation Pub Date : 2023-08-01 DOI: 10.1007/s42967-023-00274-w

Rémi Abgrall, Fatemeh Nassajian Mojarrad

引用次数: 0