Results 41 to 50 of about 397 (150)

Accelerating Conjugate Gradient Solvers for Homogenization Problems With Unitary Neural Operators

International Journal for Numerical Methods in Engineering, Volume 127, Issue 5, 15 March 2026.
ABSTRACT Rapid and reliable solvers for parametric partial differential equations (PDEs) are needed in many scientific and engineering disciplines. For example, there is a growing demand for composites and architected materials with heterogeneous microstructures.
Julius Herb, Felix Fritzen
wiley   +1 more source

Model‐Based Interpretation of Solute Exports and Carbon Partitioning During Shale Weathering in a Mountainous Hillslope

Water Resources Research, Volume 62, Issue 3, March 2026.
Abstract The weathering of sedimentary rocks in high‐elevation catchments influences freshwater quality and the global carbon cycle. While individual biogeochemical mechanisms involved in this process are relatively well understood, quantifying their contributions to solute export and carbon fluxes under natural, transient conditions remains ...
Lucien Stolze, Dipankar Dwivedi, Carl Steefel, Sergi Molins, Wenming Dong, Curtis Beutler, Alexander Newman, Kenneth Williams   +7 more
wiley   +1 more source

Solving linear and nonlinear problems using Taylor series method

Open Computer Science
The article deals with the solution of technical initial value problems. To solve such problems, an analytical or numerical approach is possible. The analytical approach can provide an accurate result; however, it is not available for all problems and it
Veigend Petr, Nečasová Gabriela, Šátek Václav   +2 more
doaj   +1 more source

Numerical Approximation of a PDE‐Constrained Optimization Problem that Appears in Data‐Driven Computational Mechanics

International Journal for Numerical Methods in Engineering, Volume 127, Issue 4, 28 February 2026.
ABSTRACT We investigate an optimization problem that arises when working within the paradigm of Data‐Driven Computational Mechanics. In the context of the diffusion‐reaction problem, such an optimization problem seeks the continuous primal fields (gradient and flux) that are closest to some predefined discrete fields taken from a material data set. The
Pedro B. Bazon, Cristian G. Gebhardt, Gustavo C. Buscaglia, Roberto F. Ausas   +3 more
wiley   +1 more source

Distributing Load Flow Computations Across System Operators Boundaries Using the Newton–Krylov–Schwarz Algorithm Implemented in PETSc

Energies, 2018
The upward trends in renewable energy penetration, cross-border flow volatility and electricity actors’ proliferation pose new challenges in the power system management. Electricity and market operators need to increase collaboration, also in terms
Stefano Guido Rinaldo, Andrea Ceresoli, Domenico J. P. Lahaye, Marco Merlo, Miloš Cvetković, Silvia Vitiello, Gianluca Fulli   +6 more
doaj   +1 more source

Multi‐Scale Electrical Conductivity Model of the Contiguous United States

Geophysical Research Letters, Volume 53, Issue 4, 28 February 2026.
Abstract The completion of the Magnetotelluric (MT) USArray across the contiguous US enables continental‐scale 3‐D imaging of the asthenosphere‐lithosphere electrical structure. We present a novel 3‐D model of the contiguous United States (MECMUS), derived from a single inversion of the now‐completed USMTArray data set.
Federico D. Munch, Alexander Grayver
wiley   +1 more source

Automated Performance Analysis with PETSc

, 2019
Comparing the performance of different discretizations or complex solvers is a challenging task, since pure flop rates or rooflines shed little light. Our recently developed TAS system for performance comparison incorporates error measures into the performance analysis, so that we can compare different solvers, discretizations, and models for the same ...
Knepley, Matthew, Chang, Justin, Cowie, Albert   +2 more
openaire   +1 more source

A Jacobian‐Free Newton‐Krylov Method for Cell‐Centred Finite Volume Solid Mechanics

International Journal for Numerical Methods in Engineering, Volume 127, Issue 3, 15 February 2026.
ABSTRACT This study proposes a Jacobian‐free Newton‐Krylov approach for finite‐volume solid mechanics. Traditional Newton‐based approaches require explicit Jacobian matrix formation and storage, which can be computationally expensive and memory‐intensive.
Philip Cardiff, Dylan Armfield, Željko Tuković, Ivan Batistić   +3 more
wiley   +1 more source

FEniCSx-pctools: Tools for PETSc Block Linear Algebra Preconditioning in FEniCSx

Journal of Open Research Software
Discretising partial differential equations with the finite element method leads to large linear systems of equations that must be solved. When these systems have a natural block structure due to multiple field variables, using iterative solvers with ...
Martin Řehoř, Jack S. Hale
doaj   +1 more source

Preliminary verification of incompressible Navier-Stokes equations solved by The Newton method

International Journal of Advanced Nuclear Reactor Design and Technology, 2020
The thermal-hydraulics module for reactor multi-physics coupling is studied. Multi-physics coupling for high temperature gas cooling reactor is very important due to the interaction between different physics, especially neutronics and thermal-hydraulics.
Juanjuan Guo, Shuoting Zhang, Changjiang Yang, Jun Wang, Shanfang Huang, Kan Wang   +5 more
doaj   +1 more source