{"title":"Accurate Absorbing Boundary Conditions for the Two-Dimensional Nonlocal Schrödinger Equations","authors":"Gang Pang, Songsong Ji, Jiwei Zhang","doi":"10.1137/21m1442048","DOIUrl":"https://doi.org/10.1137/21m1442048","url":null,"abstract":"","PeriodicalId":21812,"journal":{"name":"SIAM J. Sci. Comput.","volume":"21 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89694382","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}
{"title":"Row Replicated Block Cimmino","authors":"I. Duff, P. Leleux, Daniel J. Ruiz, F. S. Torun","doi":"10.1137/22m1487710","DOIUrl":"https://doi.org/10.1137/22m1487710","url":null,"abstract":"","PeriodicalId":21812,"journal":{"name":"SIAM J. Sci. Comput.","volume":"65 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78800760","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}
Pub Date : 2023-07-07DOI: 10.1007/s10915-023-02270-x
Tianyang Chu, Jilu Wang, Nan Wang, Zhimin Zhang
{"title":"Optimal-Order Convergence of a Two-Step BDF Method for the Navier-Stokes Equations with H1 Initial Data","authors":"Tianyang Chu, Jilu Wang, Nan Wang, Zhimin Zhang","doi":"10.1007/s10915-023-02270-x","DOIUrl":"https://doi.org/10.1007/s10915-023-02270-x","url":null,"abstract":"","PeriodicalId":21812,"journal":{"name":"SIAM J. Sci. Comput.","volume":"65 1","pages":"62"},"PeriodicalIF":0.0,"publicationDate":"2023-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76268505","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}
{"title":"Fast Computing Approaches Based on a Bilinear Pseudo-Spectral Method for Nonlinear Acoustic Wave Equations","authors":"M. Khasi, J. Rashidinia, M. Rasoulizadeh","doi":"10.1137/22m1506390","DOIUrl":"https://doi.org/10.1137/22m1506390","url":null,"abstract":"","PeriodicalId":21812,"journal":{"name":"SIAM J. Sci. Comput.","volume":"21 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87361995","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}
Pub Date : 2023-07-05DOI: 10.48550/arXiv.2206.01883
W. Bao, Yifei Li
. For the evolution of a closed surface under anisotropic surface diffusion with a general anisotropic surface energy γ ( n ) in three dimensions (3D), where n is the unit outward normal vector, by introducing a novel symmetric positive definite surface energy matrix Z k ( n ) depending on a stabilizing function k ( n ) and the Cahn-Hoffman ξ -vector, we present a new symmetrized variational formulation for anisotropic surface diffusion with weakly or strongly anisotropic surface energy, which preserves two important structures including volume conservation and energy dissipation. Then we propose a structural-preserving parametric finite element method (SP-PFEM) to discretize the symmetrized variational problem, which preserves the volume in the discretized level. Under a relatively mild and simple condition on γ ( n ), we show that SP-PFEM is unconditionally energy- stable for almost all anisotropic surface energies γ ( n ) arising in practical applications. Extensive numerical results are reported to demonstrate the efficiency and accuracy as well as energy dissipation of the proposed SP-PFEM for solving anisotropic surface diffusion in 3D.
． 对于具有一般各向异性表面能γ (n)的封闭表面在三维(3D)中的演化，其中n为单位向外法向量，通过引入依赖于稳定函数k (n)和Cahn-Hoffman ξ向量的对称正定表面能矩阵Z k (n)，我们给出了具有弱或强各向异性表面能的各向异性表面扩散的新的对称变分公式。它保留了两个重要的结构:体积守恒和能量耗散。在此基础上，提出了一种保持结构的参数有限元法(SP-PFEM)对对称变分问题进行离散化，在离散化水平上保持了体积。在相对温和和简单的γ (n)条件下，我们证明SP-PFEM对于实际应用中产生的几乎所有各向异性γ (n)表面能都是无条件能量稳定的。大量的数值结果表明，所提出的SP-PFEM在求解三维各向异性表面扩散时的效率、精度和能量消耗都得到了验证。
{"title":"A symmetrized parametric finite element method for anisotropic surface diffusion ii. three dimensions","authors":"W. Bao, Yifei Li","doi":"10.48550/arXiv.2206.01883","DOIUrl":"https://doi.org/10.48550/arXiv.2206.01883","url":null,"abstract":". For the evolution of a closed surface under anisotropic surface diffusion with a general anisotropic surface energy γ ( n ) in three dimensions (3D), where n is the unit outward normal vector, by introducing a novel symmetric positive definite surface energy matrix Z k ( n ) depending on a stabilizing function k ( n ) and the Cahn-Hoffman ξ -vector, we present a new symmetrized variational formulation for anisotropic surface diffusion with weakly or strongly anisotropic surface energy, which preserves two important structures including volume conservation and energy dissipation. Then we propose a structural-preserving parametric finite element method (SP-PFEM) to discretize the symmetrized variational problem, which preserves the volume in the discretized level. Under a relatively mild and simple condition on γ ( n ), we show that SP-PFEM is unconditionally energy- stable for almost all anisotropic surface energies γ ( n ) arising in practical applications. Extensive numerical results are reported to demonstrate the efficiency and accuracy as well as energy dissipation of the proposed SP-PFEM for solving anisotropic surface diffusion in 3D.","PeriodicalId":21812,"journal":{"name":"SIAM J. Sci. Comput.","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75516158","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}
Swastik Kopparty, Noga Ron-Zewi, Shubhangi Saraf, Mary Wootters
We show new and improved list decoding properties of folded Reed-Solomon (RS) codes and multiplicity codes. Both of these families of codes are based on polynomials over finite fields, and both have been the sources of recent advances in coding theory: Folded RS codes were the first known explicit construction of capacity-achieving list decodable codes (Guruswami and Rudra, IEEE Trans. Information Theory , 2010), and multiplicity codes were the first construction of high-rate locally decodable codes (Kopparty, Saraf, and Yekhanin, J. ACM , 2014). In this work, we show that folded RS codes and multiplicity codes are in fact better than was previously known in the context of list decoding and local list decoding. Our first main result shows that folded RS codes achieve list decoding capacity with constant list sizes, independent of the block length. Prior work with constant list sizes first obtained list sizes that are polynomial in the block length, and relied on pre-encoding with subspace evasive sets to reduce the list sizes to a constant (Guruswami and Wang, IEEE Trans. Information Theory , 2012; Dvir and Lovett, STOC , 2012). The list size we obtain is (1 /ε ) O (1 /ε ) where ε is the gap to capacity, which matches the list size obtained by pre-encoding with subspace evasive sets. For our second main result, we observe that univariate multiplicity codes exhibit similar behavior, and use this, together with additional ideas, to show that multivariate multiplicity codes are locally list decodable up to their minimum distance . By known reduc-tions, this gives in turn capacity-achieving locally list decodable codes with query complexity exp( ˜ O ((log N ) 5 / 6 )). This improves on the tensor-based construction of (Hemenway, Ron-Zewi, and Wootters, SICOMP , 2019), which gave capacity-achieving locally list decodable codes of query complexity
我们展示了折叠Reed-Solomon码和多重码的新的和改进的列表解码特性。这两种码族都基于有限域上的多项式，并且都是编码理论最新进展的来源:折叠RS码是已知的第一个明确的容量实现列表可解码码(Guruswami和Rudra, IEEE Trans)。信息论，2010)，多重码是高速率局部可解码码的首次构建(Kopparty, Saraf, and Yekhanin, J. ACM, 2014)。在这项工作中，我们表明折叠RS码和多重码实际上比以前已知的在列表解码和本地列表解码的背景下更好。我们的第一个主要结果表明，折叠RS码在列表大小不变的情况下实现了与块长度无关的列表解码能力。先前使用恒定列表大小的工作首先获得了块长度的多项式列表大小，并依赖于子空间回避集的预编码将列表大小减小到常数(Guruswami和Wang, IEEE Trans)。信息理论，2012;Dvir and Lovett, STOC, 2012)。我们得到的列表大小为(1 /ε) O (1 /ε)，其中ε为容量缺口，它与用子空间回避集预编码得到的列表大小相匹配。对于我们的第二个主要结果，我们观察到单变量多重码表现出类似的行为，并使用这一点，以及其他想法，来表明多元多重码在其最小距离内是局部列表可解码的。通过已知的约简，这反过来给出了具有查询复杂度exp(≈O ((log N) 5 / 6))的局部列表可解码代码的容量实现。这改进了基于张量的构造(Hemenway, Ron-Zewi, and wooters, SICOMP, 2019)，它提供了查询复杂性的容量实现局部列表可解码代码
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Arnab Bhattacharyya, Sutanu Gayen, Eric Price, V. Tan, N. V. Vinodchandran
{"title":"Near-Optimal Learning of Tree-Structured Distributions by Chow and Liu","authors":"Arnab Bhattacharyya, Sutanu Gayen, Eric Price, V. Tan, N. V. Vinodchandran","doi":"10.1137/22m1489678","DOIUrl":"https://doi.org/10.1137/22m1489678","url":null,"abstract":"","PeriodicalId":21812,"journal":{"name":"SIAM J. Sci. Comput.","volume":"33 1","pages":"761-793"},"PeriodicalIF":0.0,"publicationDate":"2023-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73271043","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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