{"title":"Dimensionality Reduction and Physics-Informed Neural Networks for Climate Land Models.","authors":"K. Sargsyan, C. Safta, Ricciuto Daniel","doi":"10.2172/1854072","DOIUrl":"https://doi.org/10.2172/1854072","url":null,"abstract":"","PeriodicalId":149846,"journal":{"name":"Proposed for presentation at the SIAM conference on Computational Science and Engineering held March 1-5, 2021.","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125535056","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":"Evaluating improving and maintaining a performance portable land-ice model using Albany Trilinos and Kokkos.","authors":"Jerry Watkins, Max Carlson, I. Tezaur, Kyle Shan","doi":"10.2172/1854325","DOIUrl":"https://doi.org/10.2172/1854325","url":null,"abstract":"","PeriodicalId":149846,"journal":{"name":"Proposed for presentation at the SIAM conference on Computational Science and Engineering held March 1-5, 2021.","volume":"26 3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129749000","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":"Mixed-Precision Schemes for Linear Algebra Kernels on GPUs.","authors":"G. Moon, S. Rajamanickam","doi":"10.2172/1854428","DOIUrl":"https://doi.org/10.2172/1854428","url":null,"abstract":"","PeriodicalId":149846,"journal":{"name":"Proposed for presentation at the SIAM conference on Computational Science and Engineering held March 1-5, 2021.","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128708430","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":"On the Design of Diffuse Acoustic Fields: A PDE-Constrained Optimization Approach.","authors":"W. Aquino, J. Rouse, M. Bonnet","doi":"10.2172/1854068","DOIUrl":"https://doi.org/10.2172/1854068","url":null,"abstract":"","PeriodicalId":149846,"journal":{"name":"Proposed for presentation at the SIAM conference on Computational Science and Engineering held March 1-5, 2021.","volume":"70 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115297250","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":"Pressio: A Computational Framework Enabling Projection-Based Model Reduction for Large-Scale Nonlinear Dynamical Systems.","authors":"P. Blonigan, F. Rizzi, E. Parish, John Tencer","doi":"10.2172/1853851","DOIUrl":"https://doi.org/10.2172/1853851","url":null,"abstract":"","PeriodicalId":149846,"journal":{"name":"Proposed for presentation at the SIAM conference on Computational Science and Engineering held March 1-5, 2021.","volume":"76 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127289762","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":"Use of Model Discrepancy and Model Selection as a Means of Informing Missing Physics.","authors":"K. Maupin, Teresa Portone","doi":"10.2172/1848042","DOIUrl":"https://doi.org/10.2172/1848042","url":null,"abstract":"","PeriodicalId":149846,"journal":{"name":"Proposed for presentation at the SIAM conference on Computational Science and Engineering held March 1-5, 2021.","volume":"121 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134303052","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":"Hyper-Differential Sensitivity Analysis for Robust Machine Learned Surrogate Models.","authors":"Joseph L. Hart","doi":"10.2172/1847611","DOIUrl":"https://doi.org/10.2172/1847611","url":null,"abstract":"","PeriodicalId":149846,"journal":{"name":"Proposed for presentation at the SIAM conference on Computational Science and Engineering held March 1-5, 2021.","volume":"143 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122890451","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}
The focus of this study is on spectral equivalence results for higher‚order tensor product finite elements in the H (curl), H (div), and L function spaces. For certain choices of the higher‚order shape functions, the resulting mass and stiffness matrices are spectrally equivalent to those for an assembly of lowest‚order edge‚, face‚ or interior‚based elements on the associated Gauss‚Lobatto‚Legendre ̆GLL ̄ mesh. This equivalence will help enable the development of efficient domain decomposition or multigrid preconditioners. Specifically, preconditioners for the equivalent lowest‚ order linear system can be used for the higher‚order problem and avoid the demands of assembling a higher‚order coefficient matrix. Using assemblies of lowest‚order ̆linear ̄ elements for efficient preconditioning of higher‚order discretizations in the function space H is not new. We refer the interested reader to Section 7.1 of [10] or the introduction of [2] for a discussion of the pioneering work by Orszag [9], Deville and Mund [3, 8], Canuto [1] and others. We are, however, not aware of similar approaches for problems using higher‚order edge‚ ̆Nédélec ̄, face‚ ̆Raviart‚Thomas ̄ or interior‚based elements. We note for the case of nodal elements that the degrees of freedom ̆DOFs ̄ for a higher‚order element and its equivalent assembly of lowest‚order elements are nodal values in both cases. This natural one‚to‚one correspondence of DOFs can be realized for edge‚, face‚ and interior‚based elements by using shape functions ̆bases ̄ associated with integrals and introduced by Gerritsma [5]. For edge‚based elements, the DOFs for the shape functions are associated with integrals of tangential components of a vector field along each edge of the associated GLL mesh ̆see Figure 1 left ̄. Similarly, DOFs for face‚based elements correspond to integrals of the normal component of a vector field over individual faces of the GLL mesh ̆see Figure 1 right ̄. For completeness, we also present shape functions
本研究的重点是H(旋度)、H (div)和L函数空间中高阶张量积有限元的谱等价结果。对于高阶形状函数的某些选择，所得到的质量和刚度矩阵在谱上等效于基于相关高斯、Lobatto、Legendre、GLL网格的最低阶边缘、面或内部元素的组装。这种等效性将有助于开发高效的域分解或多网格预处理器。具体而言，等效最低阶线性系统的预调节器可用于高阶问题，避免了组装高阶系数矩阵的要求。在函数空间H中使用最低阶线性元素的集合来有效地预处理更高阶离散化并不是什么新鲜事。我们建议感兴趣的读者参阅[10]的7.1节或[2]的介绍，以讨论Orszag [9]， Deville和Mund [3,8]， Canuto[1]等人的开创性工作。然而，我们还没有发现类似的方法来解决使用更高阶的边缘、n / n / n / n / n / n / n / n / n / n / n / n / n / n / n的问题。我们注意到在节点元素的情况下，高阶元素的自由度和低阶元素的等效组合在两种情况下都是节点值。通过使用由Gerritsma[5]引入的与积分相关的形状函数(shape functions) [bases]，可以实现基于边缘、面和内部元素的这种自然的一到一的自由度对应。对于基于边缘的元素，形状函数的自由度与矢量场沿相关GLL网格的每个边缘的切向分量的积分相关联(参见图1左)。类似地，基于面的元素的自由度对应于GLL网格的单个面上向量场的法向分量的积分(见图1右)。为了完整性，我们也给出了形状函数
{"title":"Spectral Equivalence Properties of Higher-Order Tensor Product Finite Elements and Applications to Preconditioning.","authors":"C. Dohrmann","doi":"10.2172/1761047","DOIUrl":"https://doi.org/10.2172/1761047","url":null,"abstract":"The focus of this study is on spectral equivalence results for higher‚order tensor product finite elements in the H (curl), H (div), and L function spaces. For certain choices of the higher‚order shape functions, the resulting mass and stiffness matrices are spectrally equivalent to those for an assembly of lowest‚order edge‚, face‚ or interior‚based elements on the associated Gauss‚Lobatto‚Legendre ̆GLL ̄ mesh. This equivalence will help enable the development of efficient domain decomposition or multigrid preconditioners. Specifically, preconditioners for the equivalent lowest‚ order linear system can be used for the higher‚order problem and avoid the demands of assembling a higher‚order coefficient matrix. Using assemblies of lowest‚order ̆linear ̄ elements for efficient preconditioning of higher‚order discretizations in the function space H is not new. We refer the interested reader to Section 7.1 of [10] or the introduction of [2] for a discussion of the pioneering work by Orszag [9], Deville and Mund [3, 8], Canuto [1] and others. We are, however, not aware of similar approaches for problems using higher‚order edge‚ ̆Nédélec ̄, face‚ ̆Raviart‚Thomas ̄ or interior‚based elements. We note for the case of nodal elements that the degrees of freedom ̆DOFs ̄ for a higher‚order element and its equivalent assembly of lowest‚order elements are nodal values in both cases. This natural one‚to‚one correspondence of DOFs can be realized for edge‚, face‚ and interior‚based elements by using shape functions ̆bases ̄ associated with integrals and introduced by Gerritsma [5]. For edge‚based elements, the DOFs for the shape functions are associated with integrals of tangential components of a vector field along each edge of the associated GLL mesh ̆see Figure 1 left ̄. Similarly, DOFs for face‚based elements correspond to integrals of the normal component of a vector field over individual faces of the GLL mesh ̆see Figure 1 right ̄. For completeness, we also present shape functions","PeriodicalId":149846,"journal":{"name":"Proposed for presentation at the SIAM conference on Computational Science and Engineering held March 1-5, 2021.","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121848931","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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