Results 11 to 20 of about 21,388 (184)

Nonlocal Operator Method for Solving Partial Differential Equations: State-of-the-Art Review and Future Perspectives

Journal of Advanced Engineering and Computation, 2022
The nonlocal operator method (NOM) is based on nonlocal theory and employs nonlocal operators of integral form to replace the local partial differential operators.
Yongzheng Zhang, H. Ren, T. Rabczuk
semanticscholar   +1 more source

An operator splitting scheme for the fractional kinetic Fokker-Planck equation [PDF]

, 2018
In this paper, we develop an operator splitting scheme for the fractional kinetic Fokker-Planck equation (FKFPE). The scheme consists of two phases: a fractional diffusion phase and a kinetic transport phase.
Duong, Manh Hong, Lu, Yulong
core   +2 more sources

PDEs with Compressed Solutions [PDF]

, 2014
Sparsity plays a central role in recent developments in signal processing, linear algebra, statistics, optimization, and other fields. In these developments, sparsity is promoted through the addition of an $L^1$ norm (or related quantity) as a constraint
Caflisch, Russel E., Osher, Stanley J., Schaeffer, Hayden, Tran, Giang   +3 more
core   +3 more sources

Variational Multiscale Stabilization and the Exponential Decay of Fine-scale Correctors [PDF]

, 2015
This paper addresses the variational multiscale stabilization of standard finite element methods for linear partial differential equations that exhibit multiscale features. The stabilization is of Petrov-Galerkin type with a standard finite element trial
A. Abdulle, A. Abdulle, A. Målqvist, A. Målqvist, A. Målqvist, C. Carstensen, C. Makridakis, D. Elfverson, D. Elfverson, D. Elfverson, D. Gallistl, D. Peterseim, D.B. Szyld, G. Rozza, H. Owhadi, H. Wu, I. Babuska, I. Babuška, J.A. Cottrell, J.A. Cottrell, J.M. Melenk, J.M. Melenk, J.M. Melenk, L. Demkowicz, L. Grasedyck, L.R. Scott, M.G. Larson, M.G. Larson, O. Cessenat, P. Cummings, P. Henning, P. Henning, P. Henning, P. Henning, R. Hiptmair, R. Tezaur, T. Betcke, T. Hughes, T.J.R. Hughes, T.J.R. Hughes, U. Hetmaniuk, X. Feng   +41 more
core   +2 more sources

Analytical simulation of the nonlinear Caputo fractional equations

Partial Differential Equations in Applied Mathematics
Partial differential equations (PDEs), particularly those involving fractional derivatives, have garnered considerable attention due to their ability to model complex systems with memory and hereditary properties.
Ali Ahadi, Seyed Mostafa Mousavi, Amir Mohammad Alinia, Hossein Khademi   +3 more
doaj   +1 more source

Efficient Gluing of Numerical Continuation and a Multiple Solution Method for Elliptic PDEs

, 2014
Numerical continuation calculations for ordinary differential equations (ODEs) are, by now, an established tool for bifurcation analysis in dynamical systems theory as well as across almost all natural and engineering sciences. Although several excellent
Kuehn, Christian
core   +1 more source

A finite element method for time fractional partial differential equations [PDF]

, 2011
This is the authors' PDF version of an article published in Fractional calculus and applied analysis© 2011. The original publication is available at www.springerlink.comThis article considers the finite element method for time fractional differential ...
Ford, Neville J., Xiao, Jingyu, Yan, Yubin   +2 more
core   +1 more source

Topology and Material Optimization in Ultra‐Soft Magneto‐Active Structures: Making Advantage of Residual Anisotropies

Advanced Materials, EarlyView.
Residual magnetization induces pronounced mechanical anisotropy in ultra‐soft magnetorheological elastomers, shaping deformation and actuation even without external magnetic fields. This study introduces a computational‐experimental framework integrating magneto‐mechanical coupling into topology optimization for designing soft magnetic actuators with ...
Carlos Perez‐Garcia, Rogelio Ortigosa, Jesús Martínez‐Frutos, Daniel Garcia‐Gonzalez   +3 more
wiley   +1 more source

AutomataGPT: Transformer‐Based Forecasting and Ruleset Inference for Two‐Dimensional Cellular Automata

Advanced Science, EarlyView.
We introduce AutomataGPT, a generative pretrained transformer (GPT) trained on synthetic spatiotemporal data from 2D cellular automata to learn symbolic rules. Demonstrating strong performance on both forward and inverse tasks, AutomataGPT establishes a scalable, domain‐agnostic framework for interpretable modeling, paving the way for future ...
Jaime A. Berkovich, Noah S. David, Markus J. Buehler   +2 more
wiley   +1 more source

Compressive Space-Time Galerkin Discretizations of Parabolic Partial Differential Equations [PDF]

, 2015
We study linear parabolic initial-value problems in a space-time variational formulation based on fractional calculus. This formulation uses "time derivatives of order one half" on the bi-infinite time axis.
Larsson, Stig, Schwab, Christoph
core   +1 more source