15 citations · 53 across the 26 of their papers we have counts for
8 papers · 1 filter
Whittle-Matérn Fields with Variable Smoothness
Hamza Ruzayqat, Wenyu Lei, David Bolin +2
We introduce and analyze a nonlocal generalization of Whittle--Matérn Gaussian fields in which the smoothness parameter varies in space through the fractional order, $s=s(x)\in[\un…
H2-MG: A multigrid method for hierarchical rank structured matrices
Daria Sushnikova, George Turkiyyah, Edmond Chow +1
This paper presents a new fast iterative solver for large systems involving kernel matrices. Advantageous aspects of H2 matrix approximations and the multigrid method are hybridize…
Finite element discretizations for variable-order fractional diffusion problems
Wenyu Lei, George Turkiyyah, Omar Knio
We present a finite element scheme for fractional diffusion problems with varying diffusivity and fractional order. We consider a symmetric integral form of these nonlocal equation…
Space-Fractional Diffusion with Variable Order and Diffusivity: Discretization and Direct Solution Strategies
Hasnaa Alzahrani, George Turkiyyah, Omar Knio +1
We consider the multidimensional space-fractional diffusion equations with spatially varying diffusivity and fractional order. Significant computational challenges are encountered…
Hierarchical Matrix Approximations of Hessians Arising in Inverse Problems Governed by PDEs
Ilona Ambartsumyan, Wajih Boukaram, Tan Bui-Thanh +5
Hessian operators arising in inverse problems governed by partial differential equations (PDEs) play a critical role in delivering efficient, dimension-independent convergence for…
O(N) Hierarchical algorithm for computing the expectations of truncated multi-variate normal distributions in N dimensions
Jingfang Huang, Fuhui Fang, George Turkiyyah +3
In this paper, we study the -dimensional integral representing the expectation of a function where is the t…
Parallel accelerated cyclic reduction preconditioner for three-dimensional elliptic PDEs with variable coefficients
Gustavo Chávez, George Turkiyyah, Stefano Zampini +1
We present a robust and scalable preconditioner for the solution of large-scale linear systems that arise from the discretization of elliptic PDEs amenable to rank compression. The…
A Direct Elliptic Solver Based on Hierarchically Low-rank Schur Complements
Gustavo Chávez, George Turkiyyah, David Keyes
A parallel fast direct solver for rank-compressible block tridiagonal linear systems is presented. Algorithmic synergies between Cyclic Reduction and Hierarchical matrix arithmetic…