Operator Reconstruction in Wavelet Bases and Its Use in Partial Differential Equations

Shijun Zheng

Operator Reconstruction in Wavelet Bases and Its Use in Partial Differential Equations

Mathematical Sciences

Research output: Contribution to conference › Presentation

Abstract

<div class="line" id="line-5"> We give a survey on recent development on wavelet-based numerical solution of time-dependent partial di&fflig;erential equa-tions. The fundamental idea is to use wavelet to give sparse representations of the solution operators involved. Thus it leads to a fast algorithm for e&ffilig;cient approximation of the solution to the PDE. We demonstrate the general scheme by considering the anisotropic di&fflig;usion equation arising in thin &filig;lm image processing. Among other examples are advection-di&fflig;usion equations arising in CF D. Numerical results are presented.</div>

Original language	American English
State	Published - May 2004
Event	Joint Mathematics Meetings (JMM) - Duration: Jan 6 2017 → …

Conference

Conference	Joint Mathematics Meetings (JMM)
Period	01/6/17 → …

Keywords

Applications
Operator reconstruction
PDEs
Wavelet basis

DC Disciplines

Mathematics

Cite this

@conference{7c1897c9d5d84f46afcc86d699d79cc7,

title = "Operator Reconstruction in Wavelet Bases and Its Use in Partial Differential Equations",

abstract = " We give a survey on recent development on wavelet-based numerical solution of time-dependent partial di&fflig;erential equa-tions. The fundamental idea is to use wavelet to give sparse representations of the solution operators involved. Thus it leads to a fast algorithm for e&ffilig;cient approximation of the solution to the PDE. We demonstrate the general scheme by considering the anisotropic di&fflig;usion equation arising in thin &filig;lm image processing. Among other examples are advection-di&fflig;usion equations arising in CF D. Numerical results are presented.",

keywords = "Applications, Operator reconstruction, PDEs, Wavelet basis",

author = "Shijun Zheng",

year = "2004",

month = may,

language = "American English",

note = "Joint Mathematics Meetings (JMM) ; Conference date: 06-01-2017",

}

TY - CONF

T1 - Operator Reconstruction in Wavelet Bases and Its Use in Partial Differential Equations

AU - Zheng, Shijun

PY - 2004/5

Y1 - 2004/5

N2 - We give a survey on recent development on wavelet-based numerical solution of time-dependent partial di&fflig;erential equa-tions. The fundamental idea is to use wavelet to give sparse representations of the solution operators involved. Thus it leads to a fast algorithm for e&ffilig;cient approximation of the solution to the PDE. We demonstrate the general scheme by considering the anisotropic di&fflig;usion equation arising in thin &filig;lm image processing. Among other examples are advection-di&fflig;usion equations arising in CF D. Numerical results are presented.

AB - We give a survey on recent development on wavelet-based numerical solution of time-dependent partial di&fflig;erential equa-tions. The fundamental idea is to use wavelet to give sparse representations of the solution operators involved. Thus it leads to a fast algorithm for e&ffilig;cient approximation of the solution to the PDE. We demonstrate the general scheme by considering the anisotropic di&fflig;usion equation arising in thin &filig;lm image processing. Among other examples are advection-di&fflig;usion equations arising in CF D. Numerical results are presented.

KW - Applications

KW - Operator reconstruction

KW - PDEs

KW - Wavelet basis

UR - http://www.ams.org/meetings/international/998-65-242.pdf

M3 - Presentation

T2 - Joint Mathematics Meetings (JMM)

Y2 - 6 January 2017

ER -

Operator Reconstruction in Wavelet Bases and Its Use in Partial Differential Equations

Abstract

Conference

Keywords

DC Disciplines

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