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pro vyhledávání: '"math.NA"'
In this work, we focus on the early design phase of cruise ship hulls, where the designers are tasked with ensuring the structural resilience of the ship against extreme waves while reducing steel usage and respecting safety and manufacturing constra
Externí odkaz:
http://arxiv.org/abs/2411.09525
In this paper we consider a system of two coupled nonlinear diffusion--reaction partial differential equations (PDEs) which model the growth of biofilm and consumption of the nutrient. At the scale of interest the biofilm density is subject to a poin
Externí odkaz:
http://arxiv.org/abs/2001.00362
Low rank approximation of a matrix (hereafter LRA) is a highly important area of Numerical Linear and Multilinear Algebra and Data Mining and Analysis. One can operate with LRA at sublinear cost, that is, by using much fewer memory cells and flops th
Externí odkaz:
http://arxiv.org/abs/1906.04112
We describe a general Godunov type splitting for numerical simulations of the Fisher/Kolmogorov-Petrovski-Piskunov growth and diffusion equation in two spatial dimensions. In particular, the method is appropriate for modeling population growth and di
Externí odkaz:
http://arxiv.org/abs/1502.04483
Autor:
Marien-Lorenzo Hanot
Publikováno v:
SIAM Journal on Numerical Analysis. 61:784-811
In this paper we discretize the incompressible Navier-Stokes equations in the framework of finite element exterior calculus. We make use of the Lamb identity to rewrite the equations into a vorticity-velocity-pressure form which fits into the de Rham
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::3296f4acd186ffbcadf686ff020ed4ea
https://doi.org/10.1137/21m1443686
https://doi.org/10.1137/21m1443686
Autor:
Daniele Avitabile
Publikováno v:
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis, In press
SIAM Journal on Numerical Analysis, 61(2), 562-591. Society for Industrial and Applied Mathematics Publications
Avitabile, D 2023, ' PROJECTION METHODS FOR NEURAL FIELD EQUATIONS ', SIAM Journal on Numerical Analysis, vol. 61, no. 2, pp. 562-591 . https://doi.org/10.1137/21M1463768
SIAM Journal on Numerical Analysis, In press
SIAM Journal on Numerical Analysis, 61(2), 562-591. Society for Industrial and Applied Mathematics Publications
Avitabile, D 2023, ' PROJECTION METHODS FOR NEURAL FIELD EQUATIONS ', SIAM Journal on Numerical Analysis, vol. 61, no. 2, pp. 562-591 . https://doi.org/10.1137/21M1463768
International audience; Neural field models are nonlinear integro-differential equations for the evolution of neuronal activity, and they are a prototypical large-scale, coarse-grained neuronal model in continuum cortices. Neural fields are often sim
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::3cca92708ec3d1845a0d5cc5485123d2
http://www.scopus.com/inward/record.url?scp=85153362046&partnerID=8YFLogxK
http://www.scopus.com/inward/record.url?scp=85153362046&partnerID=8YFLogxK
Publikováno v:
FVCA 2023-Finite Volumes for Complex Applications 10
FVCA 2023-Finite Volumes for Complex Applications 10, Oct 2023, Strasbourg, France. pp.1-8
FVCA 2023-Finite Volumes for Complex Applications 10, Oct 2023, Strasbourg, France. pp.1-8
International audience; We study an atmospheric column and its discretization. Because of numerical considerations, the column must be divided into two parts: (1) a surface layer, excluded from the computational domain and parameterized, and (2) the
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a7ce980a9e9a17a7e3edd99ad8a0482f
https://inria.hal.science/hal-04097172
https://inria.hal.science/hal-04097172
Publikováno v:
Linear Algebra and its Applications. 671:67-108
Saddle point problems arise in a variety of applications, e.g., when solving the Stokes equations. They can be formulated such that the system matrix is symmetric, but indefinite, so the variational convergence theory that is usually used to prove mu
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::fa4532c148779286165f51b83285eaef
https://doi.org/10.1016/j.laa.2023.04.016
https://doi.org/10.1016/j.laa.2023.04.016
Publikováno v:
Computers & Mathematics with Applications, 143, 94-107
Computers and Mathematics with Applications, 143, 94-107. Agon Elsevier
Computers and Mathematics with Applications, 143, 94-107. Agon Elsevier
Neural closure models have recently been proposed as a method for efficiently approximating small scales in multiscale systems with neural networks. The choice of loss function and associated training procedure has a large effect on the accuracy and
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::95f44a6130f86cd8f3e8b2fa64ac862f
https://doi.org/10.1016/j.camwa.2023.04.030
https://doi.org/10.1016/j.camwa.2023.04.030
Publikováno v:
Computers & Mathematics with Applications. 143:383-396
In this work we propose an extension of physics informed supervised learning strategies to parametric partial differential equations. Indeed, even if the latter are indisputably useful in many applications, they can be computationally expensive most
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1210e8704c5f2fbd5b8d94470cad3e7f
https://doi.org/10.1016/j.camwa.2023.05.004
https://doi.org/10.1016/j.camwa.2023.05.004