scholarly journals A Partial Integral Equation (PIE) representation of coupled linear PDEs and scalable stability analysis using LMIs

Automatica ◽  
2021 ◽  
Vol 125 ◽  
pp. 109473
Author(s):  
Matthew M. Peet
Keyword(s):  
Integral Equation ◽  
Stability Analysis ◽  
Linear Pdes

STABILITY ANALYSIS OF A COLLOCATION METHOD FOR SOLVING THE RETARDED POTENTIAL INTEGRAL EQUATION

2005 ◽  
Vol 13 (02) ◽  
pp. 287-299 ◽  
Author(s):  
P. J. HARRIS ◽  
H. WANG ◽  
R. CHAKRABARTI ◽  
D. HENWOOD
Keyword(s):  
Integral Equation ◽  
Exact Solution ◽  
Stability Analysis ◽  
Boundary Element Method ◽  
Numerical Solution ◽  
Boundary Element ◽  
Collocation Method ◽  
Stability Problem ◽  
Numerical Scheme ◽  
Type Boundary

This paper deals with the numerical solution of the retarded potential integral equation using a collocation type boundary element method. This method is widely used in practice but often suffers from stability problems. The purpose of the paper is to carry out a stability analysis of the numerical scheme and examine how any instability arises. This paper will then propose a method for overcoming this stability problem. A comparison with an exact solution demonstrates that the approach proposed here is effective for the case of a sphere.

Stability Analysis of Rectangular Plates in Incompressible Flow With Fourier Multiplier Operators

2013 ◽  
Author(s):  
Kensuke Hara ◽  
Masahiro Watanabe
Keyword(s):  
Integral Equation ◽  
Stability Analysis ◽  
Fourier Multiplier ◽  
Fourier Transforms ◽  
Mixed Boundary ◽  
Computation Time ◽  
Rectangular Plates ◽  
Multiplier Operator ◽  
Fourier Multiplier Operator ◽  
Interaction Problem

This paper describes a development of a method which improves the computational efficiency for a linear stability analysis of a plate in an uniform incompressible and irrotational flow. We introduce the Fourier multiplier operator to formulate the fluid and plate interaction problem with the mixed boundary condition. In previous typical approaches, a singular integral equation often appears in the formulation of a pressure distribution on the plate. The computation time for solving the integral equation is one of the problem encountered in the stability analysis. Applying the Fourier multiplier operator to this system, the equation of the plate-fluid interaction problem can be formulated with a pair of the Fourier and the inverse Fourier transforms. Moreover, the integration to derive the equations of motion can be efficiently carried out by using the discrete Fourier transform.

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