PETSc/TAO Users Manual: Revision 3.18

Abstract

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Coupling plasma physics and chemistry in the PIC model of electric propulsion: Application to an air-breathing, low-power Hall thruster

“…The linear algebraic system derived from Eq. 4 (and including the boundary conditions) is finally solved using the Petsc package [28].…”

Transient Nuclear Criticality Excursion Analysis of Highly Dispersed Particulate Three-Phase Fluidised Systems

“…The quasi-steady state solution to the eigenvalue problem, outlined by the two-group neutron diffusion equation, described in Section 2.3, is performed using a preconditioned conjugate gradient method with an incomplete Cholesky preconditioner (Saad, 2003). For this section of the model, the sparse mass matrices and corresponding solver have been implemented using the Portable, Extensible Toolkit for Scientific Computation (PETSc) suite of data structures and routines (Balay et al, 2021).…”

Preconditioning strategies for vectorial finite element linear systems arising from phase-field models for fracture mechanics

“…7 presents the condition number evolution during the full phase-field simulations of test 1 with mesh level 1. The cond 2 (M −1 A) is calculated by employing the Lanczos iteration algorithm for eigenvalue computation (Balay et al, 2019).…”

“…provided by the Lanczos algorithm cannot be used for complete eigenvalue analysis; however it is intended here to assist in understanding the convergence behavior of the CG and to quantify the efficiency of the preconditioning operators (Balay et al, 2019, Badri et al, 2019.…”