The SMAI journal of computational mathematics最新文献

Hybrid high-order methods for flow simulations in extremely large discrete fracture networks 超大离散裂缝网络流动模拟的混合高阶方法

The SMAI journal of computational mathematics Pub Date : 2023-03-31 DOI: 10.5802/smai-jcm.92

A. Ern, Florent Hédin, G. Pichot, Nicolas Pignet

引用次数: 3

A family of second-order dissipative finite volume schemes for hyperbolic systems of conservation laws 守恒双曲系统的二阶耗散有限体积格式族

The SMAI journal of computational mathematics Pub Date : 2023-01-27 DOI: 10.5802/smai-jcm.94

M. Badsi, C. Berthon, Ludovic Martaud

引用次数: 1

Initialization of the Circulant Embedding method to speed up the generation of Gaussian random fields 初始化循环嵌入方法，加快高斯随机场的生成

The SMAI journal of computational mathematics Pub Date : 2022-12-16 DOI: 10.5802/smai-jcm.89

G. Pichot, Simon Legrand, M. Kern, Nathanael Tepakbong-Tematio

{"title":"Initialization of the Circulant Embedding method to speed up the generation of Gaussian random fields","authors":"G. Pichot, Simon Legrand, M. Kern, Nathanael Tepakbong-Tematio","doi":"10.5802/smai-jcm.89","DOIUrl":"https://doi.org/10.5802/smai-jcm.89","url":null,"abstract":". The Circulant Embedding Method (CEM) is a well known technique to generate stationary Gaussian Random Fields (GRF). The main idea is to embed the covariance matrix in a larger nested block circulant matrix, whose factorization can be rapidly computed thanks to the fast Fourier transform (FFT) algorithm. The CEM requires the extended matrix to be at least positive semidefinite which is proven to be the case if the enclosing domain is sufficiently large, as proven by Theorem 2.3 in [9] for cubic domains. In this paper, we generalize this theorem to the case of rectangular parallelepipeds. Then we propose a new initialization stage of the CEM algorithm that makes it possible to quickly jump to a domain size close to the one needed for the CEM algorithm to work. These domain size estimates are based on fitting functions. Examples of fitting functions are given for the Matérn family of covariances. These functions are inspired by our numerical simulations and by the theoretical work from [9]. The parameters estimation of the fitting functions is done numerically. Several numerical tests are performed to show the efficiency of the proposed algorithms, for both isotropic and anisotropic Matérn covariances.","PeriodicalId":376888,"journal":{"name":"The SMAI journal of computational mathematics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128928358","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}

引用次数: 0

Parallel kinetic scheme for transport equations in complex toroidal geometry 复杂环面几何输运方程的平行动力学格式

The SMAI journal of computational mathematics Pub Date : 2022-12-16 DOI: 10.5802/smai-jcm.86

M. Boileau, Bérenger Bramas, E. Franck, Romane Hélie, P. Helluy, L. Navoret

引用次数: 0

Error Guarantees for Least Squares Approximation with Noisy Samples in Domain Adaptation 域自适应中带噪声样本最小二乘逼近的误差保证

The SMAI journal of computational mathematics Pub Date : 2022-04-09 DOI: 10.5802/smai-jcm.96

Felix Bartel

{"title":"Error Guarantees for Least Squares Approximation with Noisy Samples in Domain Adaptation","authors":"Felix Bartel","doi":"10.5802/smai-jcm.96","DOIUrl":"https://doi.org/10.5802/smai-jcm.96","url":null,"abstract":"Given $n$ samples of a function $fcolon Dtomathbb C$ in random points drawn with respect to a measure $varrho_S$ we develop theoretical analysis of the $L_2(D, varrho_T)$-approximation error. For a parituclar choice of $varrho_S$ depending on $varrho_T$, it is known that the weighted least squares method from finite dimensional function spaces $V_m$, $dim(V_m) = m<infty$ has the same error as the best approximation in $V_m$ up to a multiplicative constant when given exact samples with logarithmic oversampling. If the source measure $varrho_S$ and the target measure $varrho_T$ differ we are in the domain adaptation setting, a subfield of transfer learning. We model the resulting deterioration of the error in our bounds. Further, for noisy samples, our bounds describe the bias-variance trade off depending on the dimension $m$ of the approximation space $V_m$. All results hold with high probability. For demonstration, we consider functions defined on the $d$-dimensional cube given in unifom random samples. We analyze polynomials, the half-period cosine, and a bounded orthonormal basis of the non-periodic Sobolev space $H_{mathrm{mix}}^2$. Overcoming numerical issues of this $H_{text{mix}}^2$ basis, this gives a novel stable approximation method with quadratic error decay. Numerical experiments indicate the applicability of our results.","PeriodicalId":376888,"journal":{"name":"The SMAI journal of computational mathematics","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126397414","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}

引用次数: 1

Discrete analysis of Schwarz waveform relaxation for a diffusion reaction problem with discontinuous coefficients 具有不连续系数的扩散反应问题的Schwarz波形松弛的离散分析

The SMAI journal of computational mathematics Pub Date : 2022-04-08 DOI: 10.5802/smai-jcm.81

Simon Clément, F. Lemarié, E. Blayo

{"title":"Discrete analysis of Schwarz waveform relaxation for a diffusion reaction problem with discontinuous coefficients","authors":"Simon Clément, F. Lemarié, E. Blayo","doi":"10.5802/smai-jcm.81","DOIUrl":"https://doi.org/10.5802/smai-jcm.81","url":null,"abstract":". In this paper, we investigate the eﬀect of the space and time discretisation on the convergence properties of Schwarz Waveform Relaxation (SWR) algorithms. We consider a reaction-diﬀusion problem with discontinuous coeﬃcients discretised on two non-overlapping domains with several numerical schemes (in space and time). A methodology to determine the rate of convergence of the classical SWR method with standard interface conditions (Dirichlet-Neumann or Robin-Robin) accounting for discretisation errors is presented. We discuss how such convergence rates diﬀer from the ones derived at a continuous level (i.e. assuming an exact discrete representation of the continuous problem). In this work we consider a second-order ﬁnite diﬀerence scheme and a ﬁnite volume scheme based on quadratic spline reconstruction in space, combined with either a simple backward Euler scheme or a two-step “Padé” scheme (resembling a Diagonally Implicit Runge Kutta scheme) in time. We prove those combinations of space-time schemes to be unconditionally stable on bounded domains. We illustrate the relevance of our analysis with speciﬁcally designed numerical experiments.","PeriodicalId":376888,"journal":{"name":"The SMAI journal of computational mathematics","volume":"644 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121607385","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}

引用次数: 5

Electrostatic Force Computation with Boundary Element Methods 用边界元法计算静电力

The SMAI journal of computational mathematics Pub Date : 2022-04-08 DOI: 10.5802/smai-jcm.79

P. Panchal, R. Hiptmair

{"title":"Electrostatic Force Computation with Boundary Element Methods","authors":"P. Panchal, R. Hiptmair","doi":"10.5802/smai-jcm.79","DOIUrl":"https://doi.org/10.5802/smai-jcm.79","url":null,"abstract":". Boundary element methods are a well-established technique for solving linear boundary value problems for electrostatic potentials. In this context we present a novel way to approximate the forces exerted by electrostatic ﬁelds on conducting objects. Like the standard post-processing technique employing surface integrals derived from the Maxwell stress tensor the new approach solely relies on surface integrals, but, compared to the former, oﬀers better accuracy and faster convergence. The new formulas arise from the interpretation of forces ﬁelds as shape derivatives, in the spirit of the virtual work principle, combined with the adjoint approach from shape optimization. In contrast to standard formulas, they meet the continuity and smoothing requirements of abstract duality arguments, which supply a rigorous underpinning for their observed superior performance. 2020 Mathematics Subject Classiﬁcation. 65N38, 78M15, 45A05. Abstract. Boundary element methods are a well-established technique for solving bound- ary value problems for electrostatic potentials. In this context we present a novel way to ap- proximate the forces exerted by ﬁ elds on conducting objects. Like the standard post-processing technique employing surface integrals derived from the Maxwell stress tensor the new approach solely relies on surface integrals, but, compared to the former, o ﬀ ers better accuracy and faster convergence. The new formulas arise from the interpretation of forces ﬁ elds as shape derivatives, in the spirit of the virtual work principle, combined with the adjoint from shape optimiza-","PeriodicalId":376888,"journal":{"name":"The SMAI journal of computational mathematics","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130004389","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}

引用次数: 1

Recursive Estimation of a Failure Probability for a Lipschitz Function 一类Lipschitz函数失效概率的递归估计

The SMAI journal of computational mathematics Pub Date : 2021-07-28 DOI: 10.5802/smai-jcm.80

L. Bernard, A. Cohen, Arnaud Guyader Lpsm, Cermics, F. Malrieu

引用次数: 0

On motion by curvature of a network with a triple junction 论三结点网络的曲率运动

The SMAI journal of computational mathematics Pub Date : 2021-03-11 DOI: 10.5802/SMAI-JCM.70

Paola Pozzi, B. Stinner

引用次数: 4

Modified parareal method for solving the two-dimensional nonlinear shallow water equations using finite volumes 用有限体积求解二维非线性浅水方程的修正平行法

The SMAI journal of computational mathematics Pub Date : 2020-07-09 DOI: 10.5802/smai-jcm.75

J. G. C. Steinstraesser, V. Guinot, A. Rousseau

引用次数: 2