Alzahrani, Hasnaa; Turkiyyah, George; Knio, Omar; Keyes, David Space-fractional diffusion with variable order and diffusivity: discretization and direct solution strategies. (English) Zbl 1513.35511 Commun. Appl. Math. Comput. 4, No. 4, 1416-1440 (2022). Reviewer: Abdallah Bradji (Annaba) MSC: 35R11 65F55 65R20 PDFBibTeX XMLCite \textit{H. Alzahrani} et al., Commun. Appl. Math. Comput. 4, No. 4, 1416--1440 (2022; Zbl 1513.35511) Full Text: DOI arXiv
Zampini, Stefano; Boukaram, Wajih; Turkiyyah, George; Knio, Omar; Keyes, David H2Opus: a distributed-memory multi-GPU software package for non-local operators. (English) Zbl 1492.65003 Adv. Comput. Math. 48, No. 3, Paper No. 31, 32 p. (2022). MSC: 65-04 65Y05 65F55 65R20 PDFBibTeX XMLCite \textit{S. Zampini} et al., Adv. Comput. Math. 48, No. 3, Paper No. 31, 32 p. (2022; Zbl 1492.65003) Full Text: DOI arXiv
Huang, Jingfang; Cao, Jian; Fang, Fuhui; Genton, Marc G.; Keyes, David E.; Turkiyyah, George An \(O(N)\) algorithm for computing expectation of \(N\)-dimensional truncated multi-variate normal distribution. I: Fundamentals. (English) Zbl 07400547 Adv. Comput. Math. 47, No. 5, Paper No. 65, 34 p. (2021). MSC: 03D20 34B27 62H10 65C60 65D30 65T40 PDFBibTeX XMLCite \textit{J. Huang} et al., Adv. Comput. Math. 47, No. 5, Paper No. 65, 34 p. (2021; Zbl 07400547) Full Text: DOI
Cao, Jian; Genton, Marc G.; Keyes, David E.; Turkiyyah, George M. Exploiting low-rank covariance structures for computing high-dimensional normal and Student-\(t\) probabilities. (English) Zbl 1461.62014 Stat. Comput. 31, No. 1, Paper No. 2, 16 p. (2021). MSC: 62-08 62M30 65C05 PDFBibTeX XMLCite \textit{J. Cao} et al., Stat. Comput. 31, No. 1, Paper No. 2, 16 p. (2021; Zbl 1461.62014) Full Text: DOI arXiv
Cao, Jian; Genton, Marc G.; Keyes, David E.; Turkiyyah, George M. Sum of Kronecker products representation and its Cholesky factorization for spatial covariance matrices from large grids. (English) Zbl 1510.62021 Comput. Stat. Data Anal. 157, Article ID 107165, 15 p. (2021). MSC: 62-08 65F55 PDFBibTeX XMLCite \textit{J. Cao} et al., Comput. Stat. Data Anal. 157, Article ID 107165, 15 p. (2021; Zbl 1510.62021) Full Text: DOI
Boukaram, Wajih; Lucchesi, Marco; Turkiyyah, George; Le Maître, Olivier; Knio, Omar; Keyes, David Hierarchical matrix approximations for space-fractional diffusion equations. (English) Zbl 1506.65142 Comput. Methods Appl. Mech. Eng. 369, Article ID 113191, 21 p. (2020). MSC: 65M22 65Y10 PDFBibTeX XMLCite \textit{W. Boukaram} et al., Comput. Methods Appl. Mech. Eng. 369, Article ID 113191, 21 p. (2020; Zbl 1506.65142) Full Text: DOI HAL
Keyes, D. E.; Ltaief, H.; Turkiyyah, G. Hierarchical algorithms on hierarchical architectures. (English) Zbl 1462.65048 Philos. Trans. R. Soc. Lond., A, Math. Phys. Eng. Sci. 378, No. 2166, Article ID 20190055, 16 p. (2020). MSC: 65F99 15A23 PDFBibTeX XMLCite \textit{D. E. Keyes} et al., Philos. Trans. R. Soc. Lond., A, Math. Phys. Eng. Sci. 378, No. 2166, Article ID 20190055, 16 p. (2020; Zbl 1462.65048) Full Text: DOI
Ambartsumyan, Ilona; Boukaram, Wajih; Bui-Thanh, Tan; Ghattas, Omar; Keyes, David; Stadler, Georg; Turkiyyah, George; Zampini, Stefano Hierarchical matrix approximations of Hessians arising in inverse problems governed by PDEs. (English) Zbl 1453.65289 SIAM J. Sci. Comput. 42, No. 5, A3397-A3426 (2020). Reviewer: Alain Brillard (Riedisheim) MSC: 65M32 35Q93 49M25 49N45 65F10 65F99 65Y05 65Y10 78A46 PDFBibTeX XMLCite \textit{I. Ambartsumyan} et al., SIAM J. Sci. Comput. 42, No. 5, A3397--A3426 (2020; Zbl 1453.65289) Full Text: DOI arXiv
Cao, Jian; Genton, Marc G.; Keyes, David E.; Turkiyyah, George M. Hierarchical-block conditioning approximations for high-dimensional multivariate normal probabilities. (English) Zbl 1430.62094 Stat. Comput. 29, No. 3, 585-598 (2019). MSC: 62G30 62H12 65C05 PDFBibTeX XMLCite \textit{J. Cao} et al., Stat. Comput. 29, No. 3, 585--598 (2019; Zbl 1430.62094) Full Text: DOI Link
Boukaram, Wajih; Turkiyyah, George; Keyes, David Hierarchical matrix operations on GPUs. Matrix-vector multiplication and compression. (English) Zbl 1471.65027 ACM Trans. Math. Softw. 45, No. 1, Article No. 3, 28 p. (2019). MSC: 65F99 65Y10 PDFBibTeX XMLCite \textit{W. Boukaram} et al., ACM Trans. Math. Softw. 45, No. 1, Article No. 3, 28 p. (2019; Zbl 1471.65027) Full Text: DOI arXiv
Boukaram, Wajih; Turkiyyah, George; Keyes, David Randomized GPU algorithms for the construction of hierarchical matrices from matrix-vector operations. (English) Zbl 07099326 SIAM J. Sci. Comput. 41, No. 4, C339-C366 (2019). MSC: 65Fxx 68N19 68W10 68W20 68W25 PDFBibTeX XMLCite \textit{W. Boukaram} et al., SIAM J. Sci. Comput. 41, No. 4, C339--C366 (2019; Zbl 07099326) Full Text: DOI
Genton, Marc G.; Keyes, David E.; Turkiyyah, George Hierarchical decompositions for the computation of high-dimensional multivariate normal probabilities. (English) Zbl 07498945 J. Comput. Graph. Stat. 27, No. 2, 268-277 (2018). MSC: 62-XX PDFBibTeX XMLCite \textit{M. G. Genton} et al., J. Comput. Graph. Stat. 27, No. 2, 268--277 (2018; Zbl 07498945) Full Text: DOI Link
Chávez, Gustavo; Turkiyyah, George; Zampini, Stefano; Keyes, David Parallel accelerated cyclic reduction preconditioner for three-dimensional elliptic PDEs with variable coefficients. (English) Zbl 1460.65028 J. Comput. Appl. Math. 344, 760-781 (2018). MSC: 65F08 65N22 65Y05 PDFBibTeX XMLCite \textit{G. Chávez} et al., J. Comput. Appl. Math. 344, 760--781 (2018; Zbl 1460.65028) Full Text: DOI arXiv
Huang, Jingfang; Fang, Fuhui; Turkiyyah, George; Cao, Jian; Genton, Marc G.; Keyes, David E. O(N) Hierarchical algorithm for computing the expectations of truncated multi-variate normal distributions in N dimensions. arXiv:1809.08315 Preprint, arXiv:1809.08315 [math.NA] (2018). MSC: 03D20 34B27 62H10 65C60 65D30 65T40 BibTeX Cite \textit{J. Huang} et al., ``O(N) Hierarchical algorithm for computing the expectations of truncated multi-variate normal distributions in N dimensions'', Preprint, arXiv:1809.08315 [math.NA] (2018) Full Text: arXiv OA License
Chávez, Gustavo; Turkiyyah, George; Keyes, David E. A direct elliptic solver based on hierarchically low-rank Schur complements. (English) Zbl 1367.65149 Lee, Chang-Ock (ed.) et al., Domain decomposition methods in science and engineering XXIII. Proceedings of the 23rd international conference, Jeju Island, Korea, July 6–10, 2015. Cham: Springer (ISBN 978-3-319-52388-0/hbk; 978-3-319-52389-7/ebook). Lecture Notes in Computational Science and Engineering 116, 135-143 (2017). MSC: 65F05 65F50 65N22 65Y05 PDFBibTeX XMLCite \textit{G. Chávez} et al., Lect. Notes Comput. Sci. Eng. 116, 135--143 (2017; Zbl 1367.65149) Full Text: DOI arXiv
Chávez, Gustavo; Turkiyyah, George; Zampini, Stefano; Ltaief, Hatem; Keyes, David Accelerated Cyclic Reduction: A Distributed-Memory Fast Solver for Structured Linear Systems. arXiv:1701.00182 Preprint, arXiv:1701.00182 [math.AP] (2016). BibTeX Cite \textit{G. Chávez} et al., ``Accelerated Cyclic Reduction: A Distributed-Memory Fast Solver for Structured Linear Systems'', Preprint, arXiv:1701.00182 [math.AP] (2016) Full Text: DOI arXiv OA License