Mixed precision low-rank approximations and their application to block low-rank LU factorization
We introduce a novel approach to exploit mixed precision arithmetic for low-rank
approximations. Our approach is based on the observation that singular vectors associated …
approximations. Our approach is based on the observation that singular vectors associated …
Combining sparse approximate factorizations with mixed-precision iterative refinement
The standard LU factorization-based solution process for linear systems can be enhanced in
speed or accuracy by employing mixed-precision iterative refinement. Most recent work has …
speed or accuracy by employing mixed-precision iterative refinement. Most recent work has …
Parallel approximation of the maximum likelihood estimation for the prediction of large-scale geostatistics simulations
Maximum likelihood estimation is an important statistical technique for estimating missing
data, for example in climate and environmental applications, which are usually large and …
data, for example in climate and environmental applications, which are usually large and …
Step on it bringing fullwave finite-element microwave filter design up to speed
L Balewski, G Fotyga, M Mrozowski… - IEEE microwave …, 2020 - ieeexplore.ieee.org
There are many steps in the design of a microwave filter: mathematically describing the filter
characteristics, representing the circuit as a network of lumped elements or as a coupling …
characteristics, representing the circuit as a network of lumped elements or as a coupling …
HPS Cholesky: Hierarchical parallelized supernodal Cholesky with adaptive parameters
Sparse supernodal Cholesky on multi-NUMAs is challenging due to the supernode
relaxation and load balancing. In this work, we propose a novel approach to improve the …
relaxation and load balancing. In this work, we propose a novel approach to improve the …
A framework to exploit data sparsity in tile low-rank cholesky factorization
We present a general framework that couples the PaRSEC runtime system and the HiCMA
numerical library to solve challenging 3D data-sparse problems. Though formally dense …
numerical library to solve challenging 3D data-sparse problems. Though formally dense …
Solving block low-rank linear systems by LU factorization is numerically stable
Block low-rank (BLR) matrices possess a blockwise low-rank property that can be exploited
to reduce the complexity of numerical linear algebra algorithms. The impact of these low …
to reduce the complexity of numerical linear algebra algorithms. The impact of these low …
Direct frequency-domain 3D acoustic solver with intermediate data compression benchmarked against time-domain modeling for full-waveform inversion applications
V Kostin, S Solovyev, A Bakulin… - Geophysics, 2019 - pubs.geoscienceworld.org
We have developed a fast direct solver for numerical simulation of acoustic waves in 3D
heterogeneous media. The Helmholtz equation is approximated by a 27-point finite …
heterogeneous media. The Helmholtz equation is approximated by a 27-point finite …
A hierarchical fast direct solver for distributed memory machines with manycore nodes
C Augonnet, D Goudin, M Kuhn, X Lacoste, R Namyst… - 2019 - cea.hal.science
Compression techniques have revolutionized the Boundary Element Method used to solve
the Maxwell equations in frequency domain. In spite of the several orders of magnitude …
the Maxwell equations in frequency domain. In spite of the several orders of magnitude …
Sparse approximate multifrontal factorization with composite compression methods
This article presents a fast and approximate multifrontal solver for large sparse linear
systems. In a recent work by Liu et al., we showed the efficiency of a multifrontal solver …
systems. In a recent work by Liu et al., we showed the efficiency of a multifrontal solver …