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Showing 12 open source projects for "krylov"
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Krylov.jl
A Julia Basket of Hand-Picked Krylov Methods
If you use Krylov.jl in your work, please cite it using the metadata given in CITATION.cff. -
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KrylovKit.jl
Krylov methods for linear problems, eigenvalues, and singular values
A Julia package collecting a number of Krylov-based algorithms for linear problems, singular value and eigenvalue problems and the application of functions of linear maps or operators to vectors. -
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ExponentialUtilities.jl
Fast and differentiable implementations of matrix exponentials
ExponentialUtilities is a package of utility functions for matrix functions of exponential type, including functionality for the matrix exponential and phi-functions. These methods are more numerically stable, generic (thus support a wider range of number types), and faster than the matrix exponentiation tools in Julia's Base. The tools are used by the exponential integrators in OrdinaryDiffEq. The package has no external dependencies, so it can also be used independently. -
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LinearSolve.jl
High-Performance Unified Interface for Linear Solvers in Julia
LinearSolve.jl is a unified interface for the linear solving packages of Julia. It interfaces with other packages of the Julia ecosystem to make it easy to test alternative solver packages and pass small types to control algorithm swapping. It also interfaces with the ModelingToolkit.jl world of symbolic modeling to allow for automatically generating high-performance code. Performance is key: the current methods are made to be highly performant on scalar and statically sized small problems,... -
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TPLS
High Resolution Direct Numerical Simulation (DNS) of Two-Phase Flows
TPLS is a powerful and efficient 3D Direct Numerical Simulation (DNS) flow solver to simulate multiphase flows at unprecedented detail, speed and accuracy. This flow solver has been developed by Lennon Ó Náraigh (Mathematical Sciences, University College Dublin), Prashant Valluri (Engineering, University of Edinburgh), David Scott, Toni Collis and Iain Bethune (EPCC at the University of Edinburgh) and Peter Spelt (Université de Lyon1, Claude Bernard) under the aegis of several HECToR /... -
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Matrix Product State (MPS) Simulations
Numerical routines for variational matrix product state simulations.
Open Source MPS (OSMPS) is a collection of numerical routines for performing tensor network algorithms to simulate entangled, 1D many-body quantum systems. Our applications reach from ground state and excited states for statics to the dynamics of time-dependent Hamiltonians. We offer various time evolution methods with an emphasis on the support of long-range interactions through the matrix product state formalism. For more algorithms, see the list of features below. Please cite "M. L.... -
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RSchr-5
Solves one-electron Schrödinger equation, with SLEPc and PETSc
...Disctretization leads to generalized eigenvalue problem. Program RSchr-5 solves the generalized eigenvalue problem by algorithms implemented in SLEPc amd PETSc libraries. It uses Krylov-Schur algorithm from SLEPc library. The program is implemented in C++. The implementation is based on Message Passing Interface (MPI). -
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DD-AVX
DD-AVX: Library of high-precision operations accelerated by AVX
...author's page http://www.slis.tsukuba.ac.jp/~s1530534/index.html e-mail hishinuma@slis.tsukuba.ac.jp Double-Double (DD) precision operations are used to reduce rounding errors and improve the convergence of Krylov subspace methods. This library has Double-Double precision operations accelerated by AVX and AVX2. AVX and AVX2 are intel SIMD instructions. They operate four double precision operation simultaneously. This library needs to merge "Lis" for DD precision iterative solvers. Official support "Lis" version is "lis-1.4.58." After merge "lis" and "DD-AVX," the interface is same as "lis." ... -
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gabipb
A GPU-accelerated boundary integral Poisson-Boltzmann solver
This software package presents a GPU-accelerated direct-sum boundary integral method to solve the linear Poisson-Boltzmann (PB) equation. In our method, a well-posed boundary integral formulation is used to ensure the fast convergence of Krylov subspace based linear algebraic solver such as the GMRES. The molecular surfaces are discretized with flat triangles and centroid collocation. To speed up our method, we take advantage of the parallel nature of the boundary integral formulation and parallelize the schemes within CUDA shared memory architecture on GPU. The schemes use only $11N+6N_c$ size-of-double device memory for a biomolecule with $N$ triangular surface elements and $N_c$ partial charges. ... -
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hobipb
a higher-order boundary integral Poisson-Boltzmann solver
This software contains the parallel higher-order boundary integral method to solve the linear Poisson-Boltzmann (PB) equation. A well-posed boundary integral formulation is used to ensure the fast convergence of Krylov subspace linear solver such as GMRES. The molecular surfaces are first discretized with flat triangles and then converted to curved riangles with the assistance of normal information at vertices. To maintain the desired accuracy, four-point Gauss-Radau quadratures are used on regular triangles and sixteen-point Gauss-Legendre quadratures together with regularization transformations are applied on singular triangles. ... -
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NKA
Nonlinear Krylov acceleration of fixed-point and Newton-like methods
Nonlinear Krylov Acceleration (NKA) is a method for accelerating the convergence of fixed-point (Picard) iterations. Many Newton-like and inexact Newton methods are fixed point iterations. The NKA project provides the canonical implementation of the method for several programming languages. The black-box accelerator is simple to integrate into existing code. -
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sparse linear algebra library, with emphasis on preconditioned Krylov subspace methods for the solution of linear systems of equations
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