Zobrazeno 1 - 10
of 99
pro vyhledávání: '"Assyr Abdulle"'
We study the problem of drift estimation for two-scale continuous time series. We set ourselves in the framework of overdamped Langevin equations, for which a single-scale surrogate homogenized equation exists. In this setting, estimating the drift c
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::035d628573d73d57ea93f66978fc17ff
https://resolver.caltech.edu/CaltechAUTHORS:20201109-141017891
https://resolver.caltech.edu/CaltechAUTHORS:20201109-141017891
We propose a novel method for drift estimation of multiscale diffusion processes when a sequence of discrete observations is given. For the Langevin dynamics in a two-scale potential, our approach relies on the eigenvalues and the eigenfunctions of t
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6975388c68553660181a66975df0c80c
http://arxiv.org/abs/2104.10587
http://arxiv.org/abs/2104.10587
Explicit stabilized integrators are an efficient alternative to implicit or semi-implicit methods to avoid the severe timestep restriction faced by standard explicit integrators applied to stiff diffusion problems. In this paper, we provide a fully d
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c260ccce49ed6e7edcd932f4fc523e2c
https://hal.archives-ouvertes.fr/hal-03133054
https://hal.archives-ouvertes.fr/hal-03133054
Autor:
Assyr Abdulle, Andrea Di Blasio
Publikováno v:
Multiscale Modeling & Simulation. 17:399-433
A new numerical method based on numerical homogenization and model order reduction is introduced for the solution of multiscale inverse problems. We consider a class of elliptic problems with highly oscillatory tensors that varies on a microscopic sc
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::bd752b0bf696934f552d935c82da8ee4
https://doi.org/10.1137/16m1091320
https://doi.org/10.1137/16m1091320
Publikováno v:
Journal of Computational Physics. 451:110894
We introduce a local adaptive discontinuous Galerkin method for convection-diffusion-reaction equations. The proposed method is based on a coarse grid and iteratively improves the solution's accuracy by solving local elliptic problems in refined subd
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b617b0d1bcbe01cb7465955d59a0c540
https://doi.org/10.1016/j.jcp.2021.110894
https://doi.org/10.1016/j.jcp.2021.110894
Autor:
Timothée Noé Pouchon, Assyr Abdulle
Publikováno v:
SIAM Journal on Numerical Analysis. 56:2701-2730
A family of effective equations for the wave equation in locally periodic media over long time is derived. In particular, explicit formulas for the effective tensors are provided. To validate the derivation, an a priori error estimate between the eff
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b151eb9fc9fd1962bb0e5f4f786e5eb4
https://doi.org/10.1137/17m113678x
https://doi.org/10.1137/17m113678x
A local adaptive discontinuous Galerkin method for convection-diffusion-reaction equations is introduced. Departing from classical adaptive algorithms, the proposed method is based on a coarse grid and iteratively improves the accuracy of the solutio
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::b214a6cb7ffc21d656b8b158d0b95058
This paper aims at an accurate and ecient computation of eective quantities, e.g., the homogenized coecients for approximating the solu- tions to partial dierential equations with oscillatory coecients. Typical multiscale methods are based on a micro
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::2a996a5fdc078576c9095c0f1c6a478a
We present a novel algorithm based on the ensemble Kalman filter to solve inverse problems involving multiscale elliptic partial differential equations. Our method is based on numerical homogenization and finite element discretization and allows us t
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4ad741df84464ff80a5457c9b6e7f283
http://arxiv.org/abs/1908.05495
http://arxiv.org/abs/1908.05495
Autor:
Martin Huber, Assyr Abdulle
Publikováno v:
Numerische Mathematik
A discontinuous Galerkin finite element heterogeneous multiscale method is proposed for advection---diffusion problems with highly oscillatory coefficients. The method is based on a coupling of a discontinuous Galerkin discretization for an effective
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::38062264a755fa6349c7951858caf06f
http://doc.rero.ch/record/324953/files/211_2013_Article_578.pdf
http://doc.rero.ch/record/324953/files/211_2013_Article_578.pdf