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2020 – today
- 2024
[j62]Mark Ainsworth, Shuai Jiang:
Uniform Substructuring Preconditioners for High Order FEM on Triangles and the Influence of Nodal Basis Functions. SIAM J. Numer. Anal. 62(4): 1465-1491 (2024)- [j61]Mark Ainsworth, Charles Parker
:
Computing \(\boldsymbol{H}^{\boldsymbol{2}}\)-Conforming Finite Element Approximations Without Having to Implement \(\boldsymbol{C}^{\boldsymbol{1}}\)-Elements. SIAM J. Sci. Comput. 46(4): 2398- (2024) - [i10]Mark Ainsworth, Justin Dong:
Extended Galerkin neural network approximation of singular variational problems with error control. CoRR abs/2405.00815 (2024) - [i9]Mark Ainsworth, Charles Parker:
Two and three dimensional H2-conforming finite element approximations without C1-elements. CoRR abs/2406.00338 (2024) - 2023
- [j60]Mark Ainsworth, Charles Parker:
Uniform preconditioners for high order finite element approximations of planar linear elasticity. Math. Comput. 93(349): 2067-2102 (2023) - [j59]Mark Ainsworth, Charles Parker:
Statically Condensed Iterated Penalty Method for High Order Finite Element Discretizations of Incompressible Flow. SIAM J. Sci. Comput. 45(3): 3095-3120 (2023) - [i8]Mark Ainsworth, Charles Parker:
Statically Condensed Iterated Penalty Method for High Order Finite Element Discretizations of Incompressible Flow. CoRR abs/2301.01818 (2023) - [i7]Mark Ainsworth, Charles Parker:
Uniform Preconditioners for High Order Finite Element Approximations of Planar Linear Elasticity. CoRR abs/2302.04306 (2023) - [i6]Mark Ainsworth, Charles Parker:
Computing H2-conforming finite element approximations without having to implement C1-elements. CoRR abs/2311.04771 (2023) - 2022
- [j58]Mark Ainsworth, Charles Parker:
A Mass Conserving Mixed $hp$-FEM Scheme for Stokes Flow. Part III: Implementation and Preconditioning. SIAM J. Numer. Anal. 60(3): 1574-1606 (2022) - [j57]Mark Ainsworth, Shuai Jiang:
A Systematic Approach to Constructing Preconditioners for the $hp$-Version Mass Matrix on Unstructured and Hybrid Finite Element Meshes. SIAM J. Sci. Comput. 44(2): 901- (2022) - [j56]Mark Ainsworth, Yeonjong Shin:
Active Neuron Least Squares: A Training Method for Multivariate Rectified Neural Networks. SIAM J. Sci. Comput. 44(4): 2253- (2022) - 2021
- [j55]Ian T. Foster, Mark Ainsworth, Julie Bessac, Franck Cappello, Jong Choi, Sheng Di, Zichao Wendy Di, Ali Murat Gok, Hanqi Guo, Kevin A. Huck, Christopher Kelly, Scott Klasky, Kerstin Kleese van Dam, Xin Liang, Kshitij Mehta, Manish Parashar, Tom Peterka, Line Pouchard, Tong Shu, Ozan Tugluk, Hubertus Van Dam, Lipeng Wan, Matthew Wolf, Justin M. Wozniak, Wei Xu, Igor Yakushin, Shinjae Yoo, Todd S. Munson:
Online data analysis and reduction: An important Co-design motif for extreme-scale computers. Int. J. High Perform. Comput. Appl. 35(6): 617-635 (2021) - [j54]Mark Ainsworth, Charles Parker:
Preconditioning high order H2 conforming finite elements on triangles. Numerische Mathematik 148(2): 223-254 (2021) - [j53]Mark Ainsworth, Charles Parker:
Mass Conserving Mixed hp-FEM Approximations to Stokes Flow. Part I: Uniform Stability. SIAM J. Numer. Anal. 59(3): 1218-1244 (2021) - [j52]Mark Ainsworth, Charles Parker:
Mass Conserving Mixed hp-FEM Approximations to Stokes Flow. Part II: Optimal Convergence. SIAM J. Numer. Anal. 59(3): 1245-1272 (2021) - [j51]Mark Ainsworth, Shuai Jiang:
Preconditioning the Mass Matrix for High Order Finite Element Approximation on Tetrahedra. SIAM J. Sci. Comput. 43(1): A384-A414 (2021) - [j50]Mark Ainsworth, Justin Dong:
Galerkin Neural Networks: A Framework for Approximating Variational Equations with Error Control. SIAM J. Sci. Comput. 43(4): A2474-A2501 (2021) - [j49]Mark Ainsworth, Yeonjong Shin:
Plateau Phenomenon in Gradient Descent Training of RELU Networks: Explanation, Quantification, and Avoidance. SIAM J. Sci. Comput. 43(5): A3438-A3468 (2021) - [c8]Qian Gong, Xin Liang, Ben Whitney, Jong Youl Choi, Jieyang Chen, Lipeng Wan, Stéphane Ethier, Seung-Hoe Ku, Randy Michael Churchill, Choong-Seock Chang, Mark Ainsworth, Ozan Tugluk, Todd S. Munson, David Pugmire, Richard Archibald, Scott Klasky:
Maintaining Trust in Reduction: Preserving the Accuracy of Quantities of Interest for Lossy Compression. SMC 2021: 22-39 - [i5]Mark Ainsworth, Justin Dong:
Galerkin Neural Networks: A Framework for Approximating Variational Equations with Error Control. CoRR abs/2105.14094 (2021) - [i4]Mark Ainsworth, Charles Parker:
A Mass Conserving Mixed hp-FEM Scheme for Stokes Flow. Part III: Implementation and Preconditioning. CoRR abs/2109.14533 (2021) - 2020
- [j48]Jeremy Logan, Mark Ainsworth, Chuck Atkins, Jieyang Chen, Jong Choi, Junmin Gu, James Kress, Greg Eisenhauer, Berk Geveci, William F. Godoy, Mark Kim, Tahsin M. Kurç, Qing Liu, Kshitij Mehta, George Ostrouchov, Norbert Podhorszki, David Pugmire, Eric Suchyta, Nicholas Thompson, Ozan Tugluk, Lipeng Wan, Ruonan Wang, Ben Whitney, Matthew Wolf, Kesheng Wu, Scott Klasky:
Extending the Publish/Subscribe Abstraction for High-Performance I/O and Data Management at Extreme Scale. IEEE Data Eng. Bull. 43(1): 35-46 (2020) - [j47]Anna Lischke, Guofei Pang, Mamikon A. Gulian, Fangying Song, Christian Glusa, Xiaoning Zheng, Zhiping Mao, Wei Cai, Mark M. Meerschaert, Mark Ainsworth, George Em Karniadakis:
What is the fractional Laplacian? A comparative review with new results. J. Comput. Phys. 404 (2020) - [j46]Mark Ainsworth, Charles Parker:
H2-Stable Polynomial Liftings on Triangles. SIAM J. Numer. Anal. 58(3): 1867-1892 (2020) - [j45]Mark Ainsworth, Ozan Tugluk, Ben Whitney, Scott Klasky:
Multilevel Techniques for Compression and Reduction of Scientific Data - The Unstructured Case. SIAM J. Sci. Comput. 42(2): A1402-A1427 (2020) - [i3]Mark Ainsworth, Yeonjong Shin:
Plateau Phenomenon in Gradient Descent Training of ReLU networks: Explanation, Quantification and Avoidance. CoRR abs/2007.07213 (2020)
2010 – 2019
- 2019
- [j44]Mark Ainsworth, Guosheng Fu:
Dispersive Behavior of an Energy-Conserving Discontinuous Galerkin Method for the One-Way Wave Equation. J. Sci. Comput. 79(1): 209-226 (2019) - [j43]Mark Ainsworth, Shuai Jiang:
Preconditioning the Mass Matrix for High Order Finite Element Approximation on Triangles. SIAM J. Numer. Anal. 57(1): 355-377 (2019) - [j42]Mark Ainsworth, Ozan Tugluk, Ben Whitney, Scott Klasky:
Multilevel Techniques for Compression and Reduction of Scientific Data - The Multivariate Case. SIAM J. Sci. Comput. 41(2): A1278-A1303 (2019) - [j41]Mark Ainsworth, Ozan Tugluk, Ben Whitney, Scott Klasky:
Multilevel Techniques for Compression and Reduction of Scientific Data-Quantitative Control of Accuracy in Derived Quantities. SIAM J. Sci. Comput. 41(4): A2146-A2171 (2019) - 2018
- [j40]Mark Ainsworth, Ozan Tugluk, Ben Whitney, Scott Klasky:
Multilevel techniques for compression and reduction of scientific data - the univariate case. Comput. Vis. Sci. 19(5-6): 65-76 (2018) - [j39]Mark Ainsworth, Guosheng Fu:
Fully Computable a Posteriori Error Bounds for Hybridizable Discontinuous Galerkin Finite Element Approximations. J. Sci. Comput. 77(1): 443-466 (2018) - [j38]Mark Ainsworth, Christian Glusa:
Hybrid Finite Element-Spectral Method for the Fractional Laplacian: Approximation Theory and Efficient Solver. SIAM J. Sci. Comput. 40(4): A2383-A2405 (2018) - [c7]Jong Youl Choi, Choong-Seock Chang, Julien Dominski, Scott Klasky, Gabriele Merlo, Eric Suchyta, Mark Ainsworth, Bryce Allen, Franck Cappello, Michael Churchill, Philip E. Davis, Sheng Di, Greg Eisenhauer, Stéphane Ethier, Ian T. Foster, Berk Geveci, Hanqi Guo, Kevin A. Huck, Frank Jenko, Mark Kim, James Kress, Seung-Hoe Ku, Qing Liu, Jeremy Logan, Allen D. Malony, Kshitij Mehta, Kenneth Moreland, Todd S. Munson, Manish Parashar, Tom Peterka, Norbert Podhorszki, Dave Pugmire, Ozan Tugluk, Ruonan Wang, Ben Whitney, Matthew Wolf, Chad Wood:
Coupling Exascale Multiphysics Applications: Methods and Lessons Learned. eScience 2018: 442-452 - [c6]Scott Klasky, Matthew Wolf, Mark Ainsworth, Chuck Atkins, Jong Choi, Greg Eisenhauer, Berk Geveci, William F. Godoy, Mark Kim, James Kress, Tahsin M. Kurç, Qing Liu, Jeremy Logan, Arthur B. Maccabe, Kshitij Mehta, George Ostrouchov, Manish Parashar, Norbert Podhorszki, David Pugmire, Eric Suchyta, Lipeng Wan, Ruonan Wang:
A View from ORNL: Scientific Data Research Opportunities in the Big Data Age. ICDCS 2018: 1357-1368 - 2017
- [j37]Mark Ainsworth, Zhiping Mao:
Analysis and Approximation of a Fractional Cahn-Hilliard Equation. SIAM J. Numer. Anal. 55(4): 1689-1718 (2017) - [j36]Mark Ainsworth, Christian Glusa:
Is the Multigrid Method Fault Tolerant? The Two-Grid Case. SIAM J. Sci. Comput. 39(2) (2017) - [j35]Mark Ainsworth, Scott Klasky, Ben Whitney:
Compression Using Lossless Decimation: Analysis and Application. SIAM J. Sci. Comput. 39(4) (2017) - [j34]Mark Ainsworth, Christian Glusa:
Is the Multigrid Method Fault Tolerant? The Multilevel Case. SIAM J. Sci. Comput. 39(6) (2017) - [c5]Tao Lu, Eric Suchyta, David Pugmire, Jong Choi, Scott Klasky, Qing Liu, Norbert Podhorszki, Mark Ainsworth, Matthew Wolf:
Canopus: A Paradigm Shift Towards Elastic Extreme-Scale Data Analytics on HPC Storage. CLUSTER 2017: 58-69 - [c4]Ian T. Foster, Mark Ainsworth, Bryce Allen, Julie Bessac, Franck Cappello, Jong Youl Choi, Emil M. Constantinescu, Philip E. Davis, Sheng Di, Zichao Wendy Di, Hanqi Guo, Scott Klasky, Kerstin Kleese van Dam, Tahsin M. Kurç, Qing Liu, Abid Malik, Kshitij Mehta, Klaus Mueller, Todd S. Munson, George Ostrouchov, Manish Parashar, Tom Peterka, Line Pouchard, Dingwen Tao, Ozan Tugluk, Stefan M. Wild, Matthew Wolf, Justin M. Wozniak, Wei Xu, Shinjae Yoo:
Computing Just What You Need: Online Data Analysis and Reduction at Extreme Scales. Euro-Par 2017: 3-19 - [c3]Tao Lu, Eric Suchyta, Jong Youl Choi, Norbert Podhorszki, Scott Klasky, Qing Liu, David Pugmire, Matthew Wolf, Mark Ainsworth:
Canopus: Enabling Extreme-Scale Data Analytics on Big HPC Storage via Progressive Refactoring. HotStorage 2017 - [c2]Scott Klasky, Eric Suchyta, Mark Ainsworth, Qing Liu, Ben Whitney, Matthew Wolf, Jong Youl Choi, Ian T. Foster, Mark Kim, Jeremy Logan, Kshitij Mehta, Todd S. Munson, George Ostrouchov, Manish Parashar, Norbert Podhorszki, David Pugmire, Lipeng Wan:
Exacution: Enhancing Scientific Data Management for Exascale. ICDCS 2017: 1927-1937 - 2016
- [j33]Mark Ainsworth, Johnny Guzmán, Francisco-Javier Sayas:
Discrete extension operators for mixed finite element spaces on locally refined meshes. Math. Comput. 85(302): 2639-2650 (2016) - [j32]Mark Ainsworth, Manuel A. Sánchez:
Computing the Bézier Control Points of the Lagrangian Interpolant in Arbitrary Dimension. SIAM J. Sci. Comput. 38(3) (2016) - [i2]Mark Ainsworth, Christian Glusa:
Is the Multigrid Method Fault Tolerant? The Two-Grid Case. CoRR abs/1607.02497 (2016) - [i1]Mark Ainsworth, Christian Glusa:
Is the Multigrid Method Fault Tolerant? The Multilevel Case. CoRR abs/1607.08502 (2016) - 2015
- [j31]Mark Ainsworth, Gabriel R. Barrenechea, Andreas Wachtel:
Stabilization of High Aspect Ratio Mixed Finite Elements for Incompressible Flow. SIAM J. Numer. Anal. 53(2): 1107-1120 (2015) - [j30]Mohsen Zayernouri, Mark Ainsworth, George E. Karniadakis:
Tempered Fractional Sturm-Liouville EigenProblems. SIAM J. Sci. Comput. 37(4) (2015) - [c1]Mark Ainsworth, Christian Glusa:
Multigrid at Scale? ENUMATH 2015: 237-253 - 2014
- [j29]Mark Ainsworth:
Dispersive behaviour of high order finite element schemes for the one-way wave equation. J. Comput. Phys. 259: 1-10 (2014) - [j28]Mark Ainsworth:
Pyramid Algorithms for Bernstein-Bézier Finite Elements of High, Nonuniform Order in Any Dimension. SIAM J. Sci. Comput. 36(2) (2014) - 2013
- [j27]Mark Ainsworth, Alejandro Allendes, Gabriel R. Barrenechea, Richard Rankin:
On the Adaptive Selection of the Parameter in Stabilized Finite Element Approximations. SIAM J. Numer. Anal. 51(3): 1585-1609 (2013) - 2012
- [j26]Mark Ainsworth, Xinhui Ma:
Non-uniform order mixed FEM approximation: Implementation, post-processing, computable error bound and adaptivity. J. Comput. Phys. 231(2): 436-453 (2012) - 2011
- [j25]Mark Ainsworth, Tomás Vejchodský:
Fully computable robust a posteriori error bounds for singularly perturbed reaction-diffusion problems. Numerische Mathematik 119(2): 219-243 (2011) - [j24]Mark Ainsworth, Gaelle Andriamaro, Oleg Davydov:
Bernstein-Bézier Finite Elements of Arbitrary Order and Optimal Assembly Procedures. SIAM J. Sci. Comput. 33(6): 3087-3109 (2011) - 2010
- [j23]Mark Ainsworth:
A framework for obtaining guaranteed error bounds for finite element approximations. J. Comput. Appl. Math. 234(9): 2618-2632 (2010) - [j22]Mark Ainsworth, Richard Rankin:
Fully Computable Error Bounds for Discontinuous Galerkin Finite Element Approximations on Meshes with an Arbitrary Number of Levels of Hanging Nodes. SIAM J. Numer. Anal. 47(6): 4112-4141 (2010) - [j21]Mark Ainsworth, Hafiz Abdul Wajid:
Optimally Blended Spectral-Finite Element Scheme for Wave Propagation and NonStandard Reduced Integration. SIAM J. Numer. Anal. 48(1): 346-371 (2010)
2000 – 2009
- 2009
- [j20]Mark Ainsworth, Hafiz Abdul Wajid:
Dispersive and Dissipative Behavior of the Spectral Element Method. SIAM J. Numer. Anal. 47(5): 3910-3937 (2009) - 2008
- [j19]Mark Ainsworth, Richard Rankin:
Robust a posteriori error estimation for the nonconforming Fortin-Soulie finite element approximation. Math. Comput. 77(264): 1917-1939 (2008) - [j18]Mark Ainsworth, Richard Rankin:
Fully Computable Bounds for the Error in Nonconforming Finite Element Approximations of Arbitrary Order on Triangular Elements. SIAM J. Numer. Anal. 46(6): 3207-3232 (2008) - 2007
- [j17]Mark Ainsworth:
A Posteriori Error Estimation for Discontinuous Galerkin Finite Element Approximation. SIAM J. Numer. Anal. 45(4): 1777-1798 (2007) - [j16]Mark Ainsworth:
A Posteriori Error Estimation for Lowest Order Raviart-Thomas Mixed Finite Elements. SIAM J. Sci. Comput. 30(1): 189-204 (2007) - 2006
- [j15]Mark Ainsworth, Peter Monk, Wagner Muniz:
Dispersive and Dissipative Properties of Discontinuous Galerkin Finite Element Methods for the Second-Order Wave Equation. J. Sci. Comput. 27(1-3): 5-40 (2006) - 2005
- [j14]Willy Dörfler, Mark Ainsworth:
Reliable a posteriori error control for nonconforming finite element approximation of Stokes flow. Math. Comput. 74(252): 1599-1619 (2005) - [j13]Mark Ainsworth:
Robust A Posteriori Error Estimation for Nonconforming Finite Element Approximation. SIAM J. Numer. Anal. 42(6): 2320-2341 (2005) - 2004
- [j12]Mark Ainsworth:
Discrete Dispersion Relation for hp-Version Finite Element Approximation at High Wave Number. SIAM J. Numer. Anal. 42(2): 553-575 (2004) - 2003
- [j11]Mark Ainsworth, William McLean:
Multilevel diagonal scaling preconditioners for boundary element equations on locally refined meshes. Numerische Mathematik 93(3): 387-413 (2003) - [j10]Mark Ainsworth, Joe Coyle:
Conditioning of Hierarchic p-Version Nédélec Elements on Meshes of Curvilinear Quadrilaterals and Hexahedra. SIAM J. Numer. Anal. 41(2): 731-750 (2003) - 2002
- [j9]Mark Ainsworth, Katia Pinchedez:
hp-Approximation Theory for BDFM and RT Finite Elements on Quadrilaterals. SIAM J. Numer. Anal. 40(6): 2047-2068 (2002) - 2001
- [j8]Mark Ainsworth, Donald W. Kelly:
A Posteriori Error Estimators and Adaptivity for Finite Element Approximation of the Non-Homogeneous Dirichlet Problem. Adv. Comput. Math. 15(1-4): 3-23 (2001) - [j7]Mark Ainsworth, Willy Dörfler:
Fundamental Systems of Numerical Schemes for Linear Convection-Diffusion Equations and their Relationship to Accuracy. Computing 66(2): 199-229 (2001) - 2000
- [j6]Mark Ainsworth, Benqi Guo:
An additive Schwarz preconditioner for p-version boundary element approximation of the hypersingular operator in three dimensions. Numerische Mathematik 85(3): 343-366 (2000) - [j5]Mark Ainsworth, Patrick Coggins:
The Stability of Mixed hp-Finite Element Methods for Stokes Flow on High Aspect Ratio Elements. SIAM J. Numer. Anal. 38(5): 1721-1761 (2000) - [j4]Mark Ainsworth, Mark Arnold:
Construction and Analysis of Optimal Hierarchic Models of Boundary Value Problems on Thin Circular and Spherical Geometries. SIAM J. Sci. Comput. 22(2): 673-703 (2000)
1990 – 1999
- 1999
- [j3]Mark Ainsworth, David Kay:
The approximation theory for the p-version finite element method and application to non-linear elliptic PDEs. Numerische Mathematik 82(3): 351-388 (1999) - 1998
- [j2]Mark Ainsworth:
A posteriori error estimation for fully discrete hierarchic models of elliptic boundary value problems on thin domains. Numerische Mathematik 80(3): 325-362 (1998) - 1996
- [j1]Mark Ainsworth:
A Hierarchical Domain Decomposition Preconditioner for h-P Finite Element Approximation on Locally Refined Meshes. SIAM J. Sci. Comput. 17(6): 1395-1413 (1996)
Coauthor Index
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