Decay Estimates for 1-D Parabolic PDEs with Boundary Disturbances [PDF]
, 2017 In this work decay estimates are derived for the solutions of 1-D linear parabolic PDEs with disturbances at both boundaries and distributed disturbances. The decay estimates are given in the L2 and H1 norms of the solution and discontinuous disturbances
Karafyllis, Iasson, Krstic, Miroslav
core +2 more sources
Abstract robust coarse spaces for systems of PDEs via generalized eigenproblems in the overlaps [PDF]
, 2013 Coarse spaces are instrumental in obtaining scalability for domain decomposition methods for partial differential equations (PDEs). However, it is known that most popular choices of coarse spaces perform rather weakly in the presence of heterogeneities ...
AV Knyazev +24 more
core +1 more source
IGA-based Multi-Index Stochastic Collocation for random PDEs on arbitrary domains
, 2019 This paper proposes an extension of the Multi-Index Stochastic Collocation (MISC) method for forward uncertainty quantification (UQ) problems in computational domains of shape other than a square or cube, by exploiting isogeometric analysis (IGA ...
Beck, Joakim +2 more
core +1 more source
Additive domain decomposition operator splittings -- convergence analyses in a dissipative framework
, 2016 We analyze temporal approximation schemes based on overlapping domain decompositions. As such schemes enable computations on parallel and distributed hardware, they are commonly used when integrating large-scale parabolic systems.
Hansen, Eskil, Henningsson, Erik
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A mixed $\ell_1$ regularization approach for sparse simultaneous approximation of parameterized PDEs
, 2018 We present and analyze a novel sparse polynomial technique for the simultaneous approximation of parameterized partial differential equations (PDEs) with deterministic and stochastic inputs.
Dexter, Nick +2 more
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, 2018 Computational costs of numerically solving multidimensional partial differential equations (PDEs) increase significantly when the spatial dimensions of the PDEs are high, due to large number of spatial grid points. For multidimensional reaction-diffusion
Chen, Shanqin +3 more
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A least-squares implicit RBF-FD closest point method and applications to PDEs on moving surfaces
, 2019 The closest point method (Ruuth and Merriman, J. Comput. Phys. 227(3):1943-1961, [2008]) is an embedding method developed to solve a variety of partial differential equations (PDEs) on smooth surfaces, using a closest point representation of the surface ...
Ling, L. +3 more
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Spatiotemporal Reservoir Computing with a Reconfigurable Multifunctional Memristor Array
Advanced Materials, EarlyView.This study presents a hardware physical reservoir computing system using a tri‐modal memristive crossbar array. Stochastic masking, bistable nonlinear activation, and analog readout enable fully in‐memory spatiotemporal processing. Demonstrations on cellular automata, Lorenz prediction, ADHD EEG classification, and chaotic KS modeling highlight its ...
Sungho Kim +10 more
wiley +1 more source
A narrow-band unfitted finite element method for elliptic PDEs posed on surfaces [PDF]
, 2015 The paper studies a method for solving elliptic partial differential equations posed on hypersurfaces in $\mathbb{R}^N$, $N=2,3$. The method allows a surface to be given implicitly as a zero level of a level set function.
Olshanskii, Maxim A., Safin, Danil
core
Multiscale Cell–Cell Interactive Spatial Transcriptomics Analysis
Advanced Science, EarlyView.In this study, we present the MultiScale Cell‐Cell Interactive Spatial Transcriptomics Analysis method, which unites the strengths of spatially resolved deep learning techniques with a topological representation of multi‐scale cell‐cell similarity relations.
Sean Cottrell, Guo‐Wei Wei
wiley +1 more source