The mimetic finite difference method for the Landau–Lifshitz equation [PDF]
Journal of Computational Physics, 2017 The Landau-Lifshitz equation describes the dynamics of the magnetization inside ferromagnetic materials. This equation is highly nonlinear and has a non-convex constraint (the magnitude of the magnetization is constant) which pose interesting challenges in developing numerical methods.
Kim, Eugenia, Lipnikov, Konstantin
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A Stable Mimetic Finite-Difference Method for Convection-Dominated Diffusion Equations
SIAM Journal on Scientific Computing, 2023 Convection-diffusion equations arise in a variety of applications such as particle transport, electromagnetics, and magnetohydrodynamics. Simulation of the convection-dominated regime for these problems, even with high-fidelity techniques, is particularly challenging due to the presence of sharp boundary layers and shocks causing jumps and ...
James H. Adler +4 more
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Exact computation of the Maximum Entropy Potential of spiking neural networks models [PDF]
, 2014 Understanding how stimuli and synaptic connectivity in uence the statistics of spike patterns in neural networks is a central question in computational neuroscience.
Cessac, Bruno, Cofre, Rodrigo
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Numerical analysis for the pure Neumann control problem using the gradient discretisation method
, 2017 The article discusses the gradient discretisation method (GDM) for distributed optimal control problems governed by diffusion equation with pure Neumann boundary condition. Using the GDM framework enables to develop an analysis that directly applies to a
Droniou, Jerome +2 more
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On the Virtual Element Method for Topology Optimization on polygonal meshes: a numerical study [PDF]
, 2016 It is well known that the solution of topology optimization problems may be affected both by the geometric properties of the computational mesh, which can steer the minimization process towards local (and non-physical) minima, and by the accuracy of the ...
Antonietti, Paola F. +3 more
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The Mimetic Methods Toolkit: An object-oriented API for Mimetic Finite Differences
Journal of Computational and Applied Mathematics, 2014 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Eduardo J. Sanchez +2 more
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Introduction to discrete functional analysis techniques for the numerical study of diffusion equations with irregular data [PDF]
, 2015 We give an introduction to discrete functional analysis techniques for stationary and transient diffusion equations. We show how these techniques are used to establish the convergence of various numerical schemes without assuming non-physical regularity ...
Droniou, Jerome
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Enforcing the non-negativity constraint and maximum principles for diffusion with decay on general computational grids [PDF]
, 2010 In this paper, we consider anisotropic diffusion with decay, and the diffusivity coefficient to be a second-order symmetric and positive definite tensor.
Arnold +65 more
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Epidermal Patch Technologies for Integrated Healthcare and Infection Management
Advanced Healthcare Materials, EarlyView.Epidermal patches have evolved from simple wound coverings into multifunctional, skin‐conformable platforms integrating drug delivery, biosensing, and therapeutic functionalities. This review highlights their material innovations, fabrication strategies, and intelligent designs, including hydrogels, microneedles, and flexible electronics, while ...
Yuqi Wang +7 more
wiley +1 more source
Virtual Element Methods for hyperbolic problems on polygonal meshes [PDF]
, 2016 In the present paper we develop the Virtual Element Method for hyperbolic problems on polygonal meshes, considering the linear wave equations as our model problem. After presenting the semi-discrete scheme, we derive the convergence estimates in H^1 semi-
Vacca, Giuseppe
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