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PETSc Users Manual Revision 3.7

https://doi.org/10.2172/1255238
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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

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Efficient Management of Parallelism in Object-Oriented Numerical Software Libraries
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The MPI Message Passing Interface Standard
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New Rosenbrock W-Methods of Order 3 for Partial Differential Algebraic Equations of Index 1
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Implicit–Explicit Runge–Kutta Schemes and Applications to Hyperbolic Systems with Relaxation
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Using MPI: Portable parallel programming with the message-passing interface
inferredcites →https://doi.org/10.1016/j.jco.2007.01.009openalex-snapshot
Error propagation of general linear methods for ordinary differential equations
inferredcites →https://doi.org/10.1016/s0168-9274(02)00138-1openalex-snapshot
Additive Runge–Kutta schemes for convection–diffusion–reaction equations
inferredcites →https://doi.org/10.1016/s0168-9274(97)00056-1openalex-snapshot
Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations
inferredcites →https://doi.org/10.1016/s0898-1221(97)90035-3openalex-snapshot
Domain decomposition: Parallel multilevel methods for elliptic partial differential equations
inferredcites →https://doi.org/10.1016/s1352-2310(97)83212-8openalex-snapshot
Benchmarking stiff ode solvers for atmospheric chemistry problems II: Rosenbrock solvers
inferredcites →https://doi.org/10.1017/s0962492900002245openalex-snapshot
Iterative solution of linear systems
inferredcites →https://doi.org/10.1137/07070485xopenalex-snapshot
Highly Efficient Strong Stability-Preserving Runge–Kutta Methods with Low-Storage Implementations
inferredcites →https://doi.org/10.1137/080732833openalex-snapshot
Extrapolated Implicit-Explicit Time Stepping
inferredcites →https://doi.org/10.1137/0902001openalex-snapshot
Efficient Implementation of a Class of Preconditioned Conjugate Gradient Methods
inferredcites →https://doi.org/10.1137/0907058openalex-snapshot
GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
inferredcites →https://doi.org/10.1137/0910004openalex-snapshot
CGS, A Fast Lanczos-Type Solver for Nonsymmetric Linear systems
inferredcites →https://doi.org/10.1137/0911026openalex-snapshot
Hybrid Krylov Methods for Nonlinear Systems of Equations
inferredcites →https://doi.org/10.1137/0913035openalex-snapshot
Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
inferredcites →https://doi.org/10.1137/0914029openalex-snapshot
A Transpose-Free Quasi-Minimal Residual Algorithm for Non-Hermitian Linear Systems
inferredcites →https://doi.org/10.1137/0917003openalex-snapshot
Choosing the Forcing Terms in an Inexact Newton Method
inferredcites →https://doi.org/10.1137/1.9781611971200openalex-snapshot
Numerical Methods for Unconstrained Optimization and Nonlinear Equations
inferredcites →https://doi.org/10.1137/110842855openalex-snapshot
Implicit-Explicit Runge--Kutta Schemes for Hyperbolic Systems and Kinetic Equations in the Diffusion Limit
inferredcites →https://doi.org/10.1137/120876034openalex-snapshot
Implicit-Explicit Formulations of a Three-Dimensional Nonhydrostatic Unified Model of the Atmosphere (NUMA)
inferredcites →https://doi.org/10.1137/s1064827596303843openalex-snapshot
NITSOL: A Newton Iterative Solver for Nonlinear Systems
inferredcites →https://doi.org/10.1137/s106482759732678xopenalex-snapshot
A Restricted Additive Schwarz Preconditioner for General Sparse Linear Systems
inferredcites →https://doi.org/10.6028/jres.049.044openalex-snapshot
Methods of conjugate gradients for solving linear systems

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

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A length scale insensitive phase field model for brittle fracture of hyperelastic solids
inferred← citeshttps://doi.org/10.1016/j.engfracmech.2020.107516openalex-snapshot
Integral nonlocal approach to model interface decohesion in FFT solvers
inferred← citeshttps://doi.org/10.1016/j.envsoft.2021.105092openalex-snapshot
Distributed memory parallel groundwater modeling for the Netherlands Hydrological Instrument
inferred← citeshttps://doi.org/10.1016/j.epsl.2019.04.001openalex-snapshot
Seafloor expression of oceanic detachment faulting reflects gradients in mid-ocean ridge magma supply
inferred← citeshttps://doi.org/10.1016/j.geothermics.2024.103234openalex-snapshot
Numerical analysis of far-field fault reactivation induced by reservoir cooling
inferred← citeshttps://doi.org/10.1016/j.gete.2024.100608openalex-snapshot
Numerical modeling of hydro-mechanical processes during hydraulic testing of pre-existing fractures at the Grimsel Test Site, Switzerland
inferred← citeshttps://doi.org/10.1016/j.ifacol.2018.03.055openalex-snapshot
Modeling and Motion Planning for an Artificial Fishtail
inferred← citeshttps://doi.org/10.1016/j.ijheatfluidflow.2017.04.010openalex-snapshot
Fluid flow investigations within a 37 element CANDU fuel bundle supported by magnetic resonance velocimetry and computational fluid dynamics
inferred← citeshttps://doi.org/10.1016/j.ijnonlinmec.2018.09.013openalex-snapshot
Morpho-elastic model of the tortuous tumour vessels
inferred← citeshttps://doi.org/10.1016/j.ijrmms.2013.05.002openalex-snapshot
Development of a coupled thermo-hydro-mechanical model in discontinuous media for carbon sequestration
inferred← citeshttps://doi.org/10.1016/j.ijrmms.2018.08.012openalex-snapshot
Far field poroelastic response of geothermal reservoirs to hydraulic stimulation treatment: Theory and application at the Groß Schönebeck geothermal research facility
inferred← citeshttps://doi.org/10.1016/j.ijrmms.2019.05.003openalex-snapshot
Flexible and practical parallel implementation for coupled elastoplastic geomechanics and non-isothermal flow
inferred← citeshttps://doi.org/10.1016/j.ijsolstr.2017.08.017openalex-snapshot
An iterative multiscale modelling approach for nonlinear analysis of 3D composites
inferred← citeshttps://doi.org/10.1016/j.jcp.2013.11.032openalex-snapshot
Computation of probabilistic hazard maps and source parameter estimation for volcanic ash transport and dispersion
inferred← citeshttps://doi.org/10.1016/j.jcp.2014.10.058openalex-snapshot
An efficient parallel immersed boundary algorithm using a pseudo-compressible fluid solver
inferred← citeshttps://doi.org/10.1016/j.jcp.2015.12.022openalex-snapshot
Assessment of a hybrid finite element and finite volume code for turbulent incompressible flows
inferred← citeshttps://doi.org/10.1016/j.jcp.2017.02.072openalex-snapshot
Adaptive and iterative methods for simulations of nanopores with the PNP–Stokes equations
inferred← citeshttps://doi.org/10.1016/j.jcp.2017.05.043openalex-snapshot
Parallel numerical modeling of hybrid-dimensional compositional non-isothermal Darcy flows in fractured porous media
inferred← citeshttps://doi.org/10.1016/j.jcp.2018.01.006openalex-snapshot
An adaptive multi-moment FVM approach for incompressible flows
inferred← citeshttps://doi.org/10.1016/j.jcp.2018.01.022openalex-snapshot
A scalable variational inequality approach for flow through porous media models with pressure-dependent viscosity
inferred← citeshttps://doi.org/10.1016/j.jcp.2018.07.005openalex-snapshot
CHAOS: An octree-based PIC-DSMC code for modeling of electron kinetic properties in a plasma plume using MPI-CUDA parallelization
inferred← citeshttps://doi.org/10.1016/j.jcp.2019.04.068openalex-snapshot
A fast multi-layer boundary element method for direct numerical simulation of sound propagation in shallow water environments
inferred← citeshttps://doi.org/10.1016/j.jcp.2020.109746openalex-snapshot
Updating strategy of a domain decomposition preconditioner for parallel solution of dynamic fracture problems
inferred← citeshttps://doi.org/10.1016/j.jcp.2020.109793openalex-snapshot
High-order velocity and pressure wall boundary conditions in Eulerian incompressible SPH
inferred← citeshttps://doi.org/10.1016/j.jcp.2020.110081openalex-snapshot
A ghost structure finite difference method for a fractional FitzHugh-Nagumo monodomain model on moving irregular domain
inferred← citeshttps://doi.org/10.1016/j.jcp.2021.110563openalex-snapshot
High-order consistent SPH with the pressure projection method in 2-D and 3-D
inferred← citeshttps://doi.org/10.1016/j.jcp.2022.111349openalex-snapshot
Mixed-precision explicit stabilized Runge–Kutta methods for single- and multi-scale differential equations
inferred← citeshttps://doi.org/10.1016/j.jmps.2015.12.024openalex-snapshot
Multi-scale modelling of strongly heterogeneous 3D composite structures using spatial Voronoi tessellation
inferred← citeshttps://doi.org/10.1016/j.jmps.2019.06.021openalex-snapshot
Anisotropy of the effective toughness of layered media
inferred← citeshttps://doi.org/10.1016/j.jmps.2019.103745openalex-snapshot
Surface tension controls the onset of gyrification in brain organoids
inferred← citeshttps://doi.org/10.1016/j.jnucmat.2025.156038openalex-snapshot
Enabling BWR fuel rod analysis in the BISON fuel performance code
inferred← citeshttps://doi.org/10.1016/j.pepi.2017.11.004openalex-snapshot
Numerical solution of a non-linear conservation law applicable to the interior dynamics of partially molten planets
inferred← citeshttps://doi.org/10.1016/j.physd.2015.06.003openalex-snapshot
Phase field based nonlocal anisotropic damage mechanics model
inferred← citeshttps://doi.org/10.1016/j.pnucene.2019.03.040openalex-snapshot
Modal methods for the neutron diffusion equation using different spatial modes
inferred← citeshttps://doi.org/10.1016/j.proeng.2017.09.800openalex-snapshot
First benchmark of the Unstructured Grid Adaptation Working Group
inferred← citeshttps://doi.org/10.1016/j.renene.2014.11.079openalex-snapshot
Tidal resource extraction in the Pentland Firth, UK: Potential impacts on flow regime and sediment transport in the Inner Sound of Stroma
inferred← citeshttps://doi.org/10.1016/j.vascn.2013.04.004openalex-snapshot
Evaluation of an in silico cardiac safety assay: Using ion channel screening data to predict QT interval changes in the rabbit ventricular wedge
inferred← citeshttps://doi.org/10.1017/jfm.2017.390openalex-snapshot
The turbulence cascade in the near wake of a square prism
inferred← citeshttps://doi.org/10.1017/jfm.2017.54openalex-snapshot
Genesis and evolution of velocity gradients in near-field spatially developing turbulence
inferred← citeshttps://doi.org/10.1017/jfm.2018.331openalex-snapshot
Direct numerical simulation of heat transfer from a cylinder immersed in the production and decay regions of grid-element turbulence
inferred← citeshttps://doi.org/10.1017/jfm.2024.666openalex-snapshot
Flagellum pumping efficiency in shear-thinning viscoelastic fluids
inferred← citeshttps://doi.org/10.1017/pma.2023.5openalex-snapshot
Architecting materials for extremal stiffness, yield, and buckling strength
inferred← citeshttps://doi.org/10.1017/s0962492917000034openalex-snapshot
The nonlinear eigenvalue problem
inferred← citeshttps://doi.org/10.1029/2018ef000922openalex-snapshot
The Effects of Climate Change on GDP by Country and the Global Economic Gains From Complying With the Paris Climate Accord
inferred← citeshttps://doi.org/10.1029/2018wr023345openalex-snapshot
Multiresolution Large‐Eddy Simulation of an Array of Hydrokinetic Turbines in a Field‐Scale River: The Roosevelt Island Tidal Energy Project in New York City
inferred← citeshttps://doi.org/10.1029/2019jd030945openalex-snapshot
Analysis of the Spatial Nonuniformity of the Electric Field in Spectroscopic Diagnostic Methods of Atmospheric Electricity Phenomena
inferred← citeshttps://doi.org/10.1038/ncomms14358openalex-snapshot
Cooling a mechanical resonator with nitrogen-vacancy centres using a room temperature excited state spin–strain interaction
inferred← citeshttps://doi.org/10.1038/s41598-017-16178-8openalex-snapshot
PsiQuaSP–A library for efficient computation of symmetric open quantum systems
inferred← citeshttps://doi.org/10.1051/0004-6361/202243059openalex-snapshot
Numerical solutions to linear transfer problems of polarized radiation
inferred← citeshttps://doi.org/10.1051/bsgf/2020038openalex-snapshot
Control of inherited accreted lithospheric heterogeneity on the architecture and the low, long-term subsidence rate of intracratonic basins
inferred← citeshttps://doi.org/10.1051/epjconf/202124702023openalex-snapshot
A SIMPLIFIED TWO-NODE COARSE-MESH FINITE DIFFERENCE METHOD FOR PIN-WISE CALCULATION WITH SP3
inferred← citeshttps://doi.org/10.1051/matecconf/201925402032openalex-snapshot
Modeling of heat flow using commercial and authorial software on the example of a permanent magnet motor
inferred← citeshttps://doi.org/10.1061/(asce)cp.1943-5487.0000822openalex-snapshot
Computationally Efficient Simulation in Urban Mechanized Tunneling Based on Multilevel BIM Models
inferred← citeshttps://doi.org/10.1063/1.4958326openalex-snapshot
Analysis of non-equilibrium phenomena in inductively coupled plasma generators
inferred← citeshttps://doi.org/10.1063/1.4960436openalex-snapshot
An O(N) and parallel approach to integral problems by a kernel-independent fast multipole method: Application to polarization and magnetization of interacting particles
inferred← citeshttps://doi.org/10.1063/1.4979122openalex-snapshot
Conservative discretization of the Landau collision integral
inferred← citeshttps://doi.org/10.1063/1.4980833openalex-snapshot
Particle-in-cell simulations of an RF emission mechanism associated with hypervelocity impact plasmas
inferred← citeshttps://doi.org/10.1063/1.4983320openalex-snapshot
Verification of long wavelength electromagnetic modes with a gyrokinetic-fluid hybrid model in the XGC code
inferred← citeshttps://doi.org/10.1063/1.4983494openalex-snapshot
DNS investigation of the dynamical behaviour of trailing vortices in unbaffled stirred vessels at transitional Reynolds numbers
inferred← citeshttps://doi.org/10.1063/1.4989545openalex-snapshot
Parallel O(N) Stokes’ solver towards scalable Brownian dynamics of hydrodynamically interacting objects in general geometries
inferred← citeshttps://doi.org/10.1063/1.5000706openalex-snapshot
Incorporating inductances in tissue-scale models of cardiac electrophysiology
inferred← citeshttps://doi.org/10.1063/1.5003168openalex-snapshot
Multi-physics transient simulation of monolithic niobium dioxide-tantalum dioxide memristor-selector structures
inferred← citeshttps://doi.org/10.1063/5.0014489openalex-snapshot
Two-fluid and kinetic transport physics of Kelvin–Helmholtz instabilities in nonuniform low-beta plasmas
inferred← citeshttps://doi.org/10.1063/5.0045983openalex-snapshot
High-fidelity kinetic modeling of instabilities and gyromotion physics in nonuniform low-beta plasmas
inferred← citeshttps://doi.org/10.1063/5.0047842openalex-snapshot
Verification of a fully implicit particle-in-cell method for the v ∥-formalism of electromagnetic gyrokinetics in the XGC code
inferred← citeshttps://doi.org/10.1063/5.0151532openalex-snapshot
Resistive switching conducting filament electroformation with an electrothermal phase field method
inferred← citeshttps://doi.org/10.1063/5.0202986openalex-snapshot
SPLEND1D, a reduced one-dimensional model to investigate the physics of plasma detachment
inferred← citeshttps://doi.org/10.1063/5.0255884openalex-snapshot
An implementation of a high-order generalized finite difference method for solving the time-harmonic cold plasma wave equation in toroidal geometry
inferred← citeshttps://doi.org/10.1063/5.0290458openalex-snapshot
A morphologically self-consistent phase field model for the computational study of memristive thin film current – voltage hysteresis
inferred← citeshttps://doi.org/10.1080/00223131.2017.1359120openalex-snapshot
Multigroup neutron diffusion equation with the finite volume method in reactors using MOX fuels
inferred← citeshttps://doi.org/10.1080/02656736.2020.1749317openalex-snapshot
Mathematical modeling of mass and energy transport for thermoembolization
inferred← citeshttps://doi.org/10.1080/02678292.2017.1365385openalex-snapshot
Computing equilibrium states of cholesteric liquid crystals in elliptical channels with deflation algorithms
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