A survey on direct solvers for Galerkin methods
In this paper we describe the history, performance, and design concepts of direct solvers for algebraic systems resulting from Galerkin discretizations of partial differential equations. Popular direct solver implementations of Gaussian elimination (also known as LU factorization) are introduced and...
| Main Authors: | Pardo, D., Paszynski, M., Collier, N., Alvarez, J., Dalcin, L., Calo, Victor |
|---|---|
| Format: | Journal Article |
| Published: |
2012
|
| Online Access: | http://hdl.handle.net/20.500.11937/62810 |
Similar Items
The cost of continuity: A study of the performance of isogeometric finite elements using direct solvers
by: Collier, N., et al.
Published: (2012)
by: Collier, N., et al.
Published: (2012)
The value of continuity: Refined isogeometric analysis and fast direct solvers
by: Garcia, D., et al.
Published: (2016)
by: Garcia, D., et al.
Published: (2016)
Direct solvers performance on h-adapted grids
by: Paszynski, M., et al.
Published: (2015)
by: Paszynski, M., et al.
Published: (2015)
On the computational efficiency of isogeometric methods for smooth elliptic problems using direct solvers
by: Collier, N., et al.
Published: (2014)
by: Collier, N., et al.
Published: (2014)
Computational complexity and memory usage for multi-frontal direct solvers in structured mesh finite elements
by: Collier, N., et al.
Published: (2012)
by: Collier, N., et al.
Published: (2012)
Computational complexity and memory usage for multi-frontal direct solvers used in p finite element analysis
by: Calo, Victor, et al.
Published: (2011)
by: Calo, Victor, et al.
Published: (2011)
Impact of element-level static condensation on iterative solver performance
by: Pardo, D., et al.
Published: (2015)
by: Pardo, D., et al.
Published: (2015)
The cost of continuity: Performance of iterative solvers on isogeometric finite elements
by: Collier, N., et al.
Published: (2013)
by: Collier, N., et al.
Published: (2013)
A direct solver with reutilization of LU factorizations for h-adaptive finite element grids with point singularities
by: Paszynski, M., et al.
Published: (2013)
by: Paszynski, M., et al.
Published: (2013)
Computational cost of isogeometric multi-frontal solvers on parallel distributed memory machines
by: Wozniak, M., et al.
Published: (2015)
by: Wozniak, M., et al.
Published: (2015)
Refined Isogeometric Analysis for a preconditioned conjugate gradient solver
by: Garcia, D., et al.
Published: (2018)
by: Garcia, D., et al.
Published: (2018)
On round-off error for adaptive finite element methods
by: Alvarez-Aramberri, J., et al.
Published: (2012)
by: Alvarez-Aramberri, J., et al.
Published: (2012)
Parallel Fast Isogeometric Solvers for Explicit Dynamics
by: Wozniak, M., et al.
Published: (2017)
by: Wozniak, M., et al.
Published: (2017)
Graph Grammar Based Multi-Frontal Solver for Isogeometric FEM Simulations On GPU
by: Paszynski, M., et al.
Published: (2013)
by: Paszynski, M., et al.
Published: (2013)
Graph grammar based parallel direct solver for 1D and 2D isogeometric finite element method
by: Paszynski, M., et al.
Published: (2012)
by: Paszynski, M., et al.
Published: (2012)
Graph grammar-based multi-frontal parallel direct solver for two-dimensional isogeometric analysis
by: Kuznik, K., et al.
Published: (2012)
by: Kuznik, K., et al.
Published: (2012)
ICCS 2017 Workshop on Agent-Based Simulations, Adaptive Algorithms and Solvers
by: Byrski, A., et al.
Published: (2017)
by: Byrski, A., et al.
Published: (2017)
Computational cost estimates for parallel shared memory isogeometric multi-frontal solvers
by: Wozniak, M., et al.
Published: (2014)
by: Wozniak, M., et al.
Published: (2014)
Analysis of the discontinuous Petrov-Galerkin method with optimal test functions for the Reissner-Mindlin plate bending model
by: Calo, Victor, et al.
Published: (2014)
by: Calo, Victor, et al.
Published: (2014)
Discontinuous Petrov-Galerkin method based on the optimal test space norm for one-dimensional transport problems
by: Niemi, A., et al.
Published: (2011)
by: Niemi, A., et al.
Published: (2011)
Grammar based multi-frontal solver for isogeometric analysis in 1D
by: Kuznik, K., et al.
Published: (2013)
by: Kuznik, K., et al.
Published: (2013)
Automatically stable discontinuous Petrov-Galerkin methods for stationary transport problems: Quasi-optimal test space norm
by: Niemi, A., et al.
Published: (2013)
by: Niemi, A., et al.
Published: (2013)
Discontinuous Petrov-Galerkin method based on the optimal test space norm for steady transport problems in one space dimension
by: Niemi, A., et al.
Published: (2013)
by: Niemi, A., et al.
Published: (2013)
Grammar-based multi-frontal solver for one dimensional isogeometric analysis with multiple right-hand-sides
by: Kuznik, K., et al.
Published: (2013)
by: Kuznik, K., et al.
Published: (2013)
Dynamic programming algorithm for generation of optimal elimination trees for multi-frontal direct solver over h-refined grids
by: AbouEisha, H., et al.
Published: (2014)
by: AbouEisha, H., et al.
Published: (2014)
Fast isogeometric solvers for explicit dynamics
by: Gao, L., et al.
Published: (2014)
by: Gao, L., et al.
Published: (2014)
Telescopic hybrid fast solver for 3D elliptic problems with point singularities
by: Paszynska, A., et al.
Published: (2015)
by: Paszynska, A., et al.
Published: (2015)
Element Partition Trees for H-Refined Meshes to Optimize Direct Solver Performance. Part I: Dynamic Programming
by: Aboueisha, H., et al.
Published: (2017)
by: Aboueisha, H., et al.
Published: (2017)
Bisections-Weighted-by-Element-Size-and-Order Algorithm to Optimize Direct Solver Performance on 3D hp-adaptive Grids
by: AbouEisha, H., et al.
Published: (2018)
by: AbouEisha, H., et al.
Published: (2018)
A class of discontinuous Petrov-Galerkin methods. Part IV: The optimal test norm and time-harmonic wave propagation in 1D
by: Zitelli, J., et al.
Published: (2011)
by: Zitelli, J., et al.
Published: (2011)
Parallel simulations of 3d DC borehole resistivity measurements with goaloriented self-adaptive hp finite element method
by: Paszynski, M., et al.
Published: (2012)
by: Paszynski, M., et al.
Published: (2012)
Dealing with periodic boundary conditions for 1D, 2D and 3D isogeometric finite element method
by: Los, M., et al.
Published: (2015)
by: Los, M., et al.
Published: (2015)
Goal-oriented self-adaptive hp finite element simulation of 3D DC borehole resistivity simulations
by: Calo, Victor, et al.
Published: (2011)
by: Calo, Victor, et al.
Published: (2011)
Gauss–Galerkin quadrature rules for quadratic and cubic spline spaces and their application to isogeometric analysis
by: Barton, M., et al.
Published: (2017)
by: Barton, M., et al.
Published: (2017)
Modeling phase-transitions using a high-performance, isogeometric analysis framework
by: Vignal, P., et al.
Published: (2014)
by: Vignal, P., et al.
Published: (2014)
Time adaptivity in the diffusive wave approximation to the shallow water equations
by: Collier, N., et al.
Published: (2013)
by: Collier, N., et al.
Published: (2013)
Diffusive wave approximation to the shallow water equations: Computational approach
by: Collier, N., et al.
Published: (2011)
by: Collier, N., et al.
Published: (2011)
Isogeometric shell formulation based on a classical shell model
by: Niemi, A., et al.
Published: (2012)
by: Niemi, A., et al.
Published: (2012)
Micropolar nano fluids using B-spline divergence conforming spaces
by: Sarmiento, A., et al.
Published: (2014)
by: Sarmiento, A., et al.
Published: (2014)
Micropolar fluids using B-spline divergence conforming spaces
by: Sarmiento, A., et al.
Published: (2014)
by: Sarmiento, A., et al.
Published: (2014)
Similar Items
-
The cost of continuity: A study of the performance of isogeometric finite elements using direct solvers
by: Collier, N., et al.
Published: (2012) -
The value of continuity: Refined isogeometric analysis and fast direct solvers
by: Garcia, D., et al.
Published: (2016) -
Direct solvers performance on h-adapted grids
by: Paszynski, M., et al.
Published: (2015) -
On the computational efficiency of isogeometric methods for smooth elliptic problems using direct solvers
by: Collier, N., et al.
Published: (2014) -
Computational complexity and memory usage for multi-frontal direct solvers in structured mesh finite elements
by: Collier, N., et al.
Published: (2012)