On MultiScale ADI Methods for Parabolic PDEs with a Discontinuous Coefficient

Zhilin Li; Xiaohong Chen; Zhengru Zhang

doi:10.1137/17m1151985

On MultiScale ADI Methods for Parabolic PDEs with a Discontinuous Coefficient

Multiscale Modeling and Simulation ◽

10.1137/17m1151985 ◽

2018 ◽

Vol 16 (4) ◽

pp. 1623-1647 ◽

Cited By ~ 1

Author(s):

Zhilin Li ◽

Xiaohong Chen ◽

Zhengru Zhang

Keyword(s):

Discontinuous Coefficient ◽

Parabolic Pdes ◽

Adi Methods

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A stochastic collocation approach for parabolic PDEs with random domain deformations

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2021.04.005 ◽

2021 ◽

Vol 93 ◽

pp. 32-49

Author(s):

Julio E. Castrillón-Candás ◽

Jie Xu

Keyword(s):

Stochastic Collocation ◽

Parabolic Pdes ◽

Collocation Approach

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BOUNDARY CONTROL LAWS FOR PARABOLIC PDES WITH VOLTERRA NONLINEARITIES—PART I: DESIGN

IFAC Proceedings Volumes ◽

10.3182/20070822-3-za-2920.00025 ◽

2007 ◽

Vol 40 (12) ◽

pp. 146-151

Author(s):

Rafael Vazquez ◽

Miroslav Krstic

Keyword(s):

Boundary Control ◽

Parabolic Pdes ◽

Control Laws

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Adaptive stabilization for ODE systems coupled with parabolic PDES

Journal of Systems Science and Complexity ◽

10.1007/s11424-016-5094-4 ◽

2016 ◽

Vol 29 (4) ◽

pp. 959-977 ◽

Cited By ~ 1

Author(s):

Jian Li ◽

Yungang Liu

Keyword(s):

Adaptive Stabilization ◽

Parabolic Pdes ◽

Ode Systems

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Probabilistic approach for systems of second order quasi-linear parabolic PDEs

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2011.09.059 ◽

2012 ◽

Vol 388 (2) ◽

pp. 676-694 ◽

Cited By ~ 1

Author(s):

Jinxia Wang ◽

Xicheng Zhang

Keyword(s):

Probabilistic Approach ◽

Second Order ◽

Parabolic Pdes

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Output feedback control of inhomogeneous parabolic PDEs with point actuation and point measurement using SOS and semi-separable kernels

2015 54th IEEE Conference on Decision and Control (CDC) ◽

10.1109/cdc.2015.7402377 ◽

2015 ◽

Cited By ~ 2

Author(s):

Aditya Gahlawat ◽

Matthew M. Peet

Keyword(s):

Feedback Control ◽

Output Feedback ◽

Output Feedback Control ◽

Parabolic Pdes ◽

Point Measurement

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On the boundary value problem for the Sturm-Liouville equation with the discontinuous coefficient

Mathematical Methods in the Applied Sciences ◽

10.1002/mma.2714 ◽

2012 ◽

Vol 36 (13) ◽

pp. 1685-1700 ◽

Cited By ~ 9

Author(s):

A. Adiloglu Nabiev ◽

R.Kh. Amirov

Keyword(s):

Boundary Value Problem ◽

Liouville Equation ◽

Boundary Value ◽

Discontinuous Coefficient ◽

Sturm Liouville

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Solvability of boundary value problems for second-order elliptic differential-operator equations with a spectral parameter and with a discontinuous coefficient at the highest derivative

Differential Equations ◽

10.1134/s0012266114040053 ◽

2014 ◽

Vol 50 (4) ◽

pp. 464-475 ◽

Cited By ~ 1

Author(s):

B. A. Aliev ◽

Ya. Yakubov

Keyword(s):

Differential Operator ◽

Boundary Value Problems ◽

Spectral Parameter ◽

Boundary Value ◽

Second Order ◽

Discontinuous Coefficient ◽

Elliptic Differential Operator ◽

Operator Equations

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Scalar parabolic PDEs and braids

Transactions of the American Mathematical Society ◽

10.1090/s0002-9947-08-04823-x ◽

2008 ◽

Vol 361 (05) ◽

pp. 2755-2788 ◽

Cited By ~ 3

Author(s):

R. W. Ghrist ◽

R. C. Vandervorst

Keyword(s):

Parabolic Pdes

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A backstepping approach to the output regulation of boundary controlled parabolic PDEs

Automatica ◽

10.1016/j.automatica.2015.04.008 ◽

2015 ◽

Vol 57 ◽

pp. 56-64 ◽

Cited By ~ 61

Author(s):

Joachim Deutscher

Keyword(s):

Output Regulation ◽

Parabolic Pdes ◽

Backstepping Approach

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Multilevel preconditioning and low-rank tensor iteration for space-time simultaneous discretizations of parabolic PDEs

Numerical Linear Algebra with Applications ◽

10.1002/nla.1951 ◽

2014 ◽

Vol 22 (2) ◽

pp. 317-337 ◽

Cited By ~ 15

Author(s):

Roman Andreev ◽

Christine Tobler

Keyword(s):

Space Time ◽

Low Rank ◽

Parabolic Pdes ◽

Rank Tensor ◽

Multilevel Preconditioning

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