Superior properties of the PRESB preconditioner for operators on two-by-two block form with square blocks
Sign Up to like & getrecommendations! Published in 2020 at "Numerische Mathematik"
DOI: 10.1007/s00211-020-01143-x
Abstract: Matrices or operators in two-by-two block form with square blocks arise in numerous important applications, such as in optimal control problems for PDEs. The problems are normally of very large scale so iterative solution methods… read more here.
Keywords: block; operators two; two two; preconditioner ... See more keywords
Efficient preconditioner of one-sided space fractional diffusion equation
Sign Up to like & getrecommendations! Published in 2018 at "BIT Numerical Mathematics"
DOI: 10.1007/s10543-018-0699-8
Abstract: In this paper, we propose an efficient preconditioner for the linear systems arising from the one-sided space fractional diffusion equation with variable coefficients. The shifted Gr$$\ddot{\mathrm{u}}$$u¨nwald formula is employed to discretize the one-sided Riemann–Liouville fractional… read more here.
Keywords: efficient preconditioner; fractional diffusion; one sided; sided space ... See more keywords
An improved block splitting preconditioner for complex symmetric indefinite linear systems
Sign Up to like & getrecommendations! Published in 2017 at "Numerical Algorithms"
DOI: 10.1007/s11075-017-0323-z
Abstract: In this paper, an improved block splitting preconditioner for a class of complex symmetric indefinite linear systems is proposed. By adopting two iteration parameters and the relaxation technique, the new preconditioner not only remains the… read more here.
Keywords: block; splitting preconditioner; improved block; block splitting ... See more keywords
A new alternating positive semidefinite splitting preconditioner for saddle point problems from time-harmonic eddy current models
Sign Up to like & getrecommendations! Published in 2018 at "Frontiers of Mathematics in China"
DOI: 10.1007/s11464-018-0679-y
Abstract: Based on the special positive semidefinite splittings of the saddle point matrix, we propose a new alternating positive semidefinite splitting (APSS) iteration method for the saddle point problem arising from the finite element discretization of… read more here.
Keywords: topology; positive semidefinite; preconditioner; saddle point ... See more keywords
A linearized coarse mesh finite difference preconditioner for the within-group Krylov subspace iteration based on two-dimensional method of characteristics
Sign Up to like & getrecommendations! Published in 2021 at "Annals of Nuclear Energy"
DOI: 10.1016/j.anucene.2020.107889
Abstract: Abstract In this work, a preconditioner is developed based on the linear coarse mesh finite difference (CMFD) formulation for the flexible generalized minimal residual (FGMRES) algorithm, and applied to accelerate within-group Krylov iterations based on… read more here.
Keywords: within group; mesh finite; method; coarse mesh ... See more keywords
A novel linear solver for simulating highly heterogeneous black oil reservoirs
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Petroleum Science and Engineering"
DOI: 10.1016/j.petrol.2020.107506
Abstract: Abstract A great deal of computational power and time is necessary for the simulation of highly heterogeneous fractured reservoirs with complicated geometry. Simulating such largescale complex reservoirs with both minimum time and maximum accuracy has… read more here.
Keywords: highly heterogeneous; novel linear; black oil; preconditioner ... See more keywords
Sparse Approximate Inverse Preconditioner With Parametric Sparsity Pattern Applied to the Macrobasis Function Methods
Sign Up to like & getrecommendations! Published in 2018 at "IEEE Antennas and Wireless Propagation Letters"
DOI: 10.1109/lawp.2018.2819085
Abstract: An efficient approach for the generation of sparse preconditioners, tailored for the application of macrobasis function methods, is described in this letter. The preconditioner is highly scalable and generated by the computing groups of rows… read more here.
Keywords: preconditioner; macrobasis function; function methods; sparsity pattern ... See more keywords
Intelligent Seismic Deblending Through Deep Preconditioner
Sign Up to like & getrecommendations! Published in 2022 at "IEEE Geoscience and Remote Sensing Letters"
DOI: 10.1109/lgrs.2022.3193716
Abstract: Seismic deblending is an ill-posed inverse problem that involves counteracting the effect of a blending matrix derived from the shots’ position and firing time. In this letter, we propose a seismic deblending method based on… read more here.
Keywords: deblending deep; deep preconditioner; preconditioner; intelligent seismic ... See more keywords
Preconditioned Stochastic Gradient Descent
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DOI: 10.1109/tnnls.2017.2672978
Abstract: Stochastic gradient descent (SGD) still is the workhorse for many practical problems. However, it converges slow, and can be difficult to tune. It is possible to precondition SGD to accelerate its convergence remarkably. But many… read more here.
Keywords: preconditioned stochastic; gradient descent; preconditioner; gradient ... See more keywords
Investigation of High-Efficiency Iterative ILU Preconditioner Algorithm for Partial-Differential Equation Systems
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DOI: 10.3390/sym11121461
Abstract: In this paper, we investigate an iterative incomplete lower and upper (ILU) factorization preconditioner for partial-differential equation systems. We discretize the partial-differential equations into linear equation systems. An iterative scheme of linear systems is used.… read more here.
Keywords: equation systems; differential equation; partial differential; preconditioner ... See more keywords