Solution of potential flow problems by the modified method of fundamental solutions: Formulations with the single layer and the double layer fundamental solutions

2009 ◽  
Vol 33 (12) ◽  
pp. 1374-1382 ◽  
Author(s):  
Božidar Šarler
Keyword(s):  
Double Layer ◽  
Potential Flow ◽  
Single Layer ◽  
Fundamental Solutions ◽  
Method Of Fundamental Solutions ◽  
Flow Problems ◽  
Modified Method

ON THE TRUE AND SPURIOUS EIGENVALUES BY USING THE REAL OR THE IMAGINARY-PART OF THE METHOD OF FUNDAMENTAL SOLUTIONS

2013 ◽  
Vol 10 (02) ◽  
pp. 1341003 ◽  
Author(s):  
I. L. CHEN ◽  
Y. T. LEE ◽  
P. S. KUO ◽  
J. T. CHEN
Keyword(s):  
Double Layer ◽  
Imaginary Part ◽  
Single Layer ◽  
Fundamental Solutions ◽  
Method Of Fundamental Solutions ◽  
Double Layer Potential ◽  
Layer Potential ◽  
The Common ◽  
Value Decomposition ◽  
Spurious Eigenvalues

In this paper, the method of fundamental solutions (MFS) of real-part or imaginary-part kernels is employed to solve two-dimensional eigenproblems. The occurring mechanism of spurious eigenvalues for circular and elliptical membranes is examined. It is found that the spurious eigensolution using the MFS depends on the location of the fictitious boundary where the sources are distributed. By employing the singular value decomposition technique, the common left unitary vectors of the true eigenvalue for the single- and double-layer potential approaches are found while the common right unitary vectors of the spurious eigenvalue are obtained. Dirichlet and Neumann eigenproblems are both considered. True eigenvalues are dependent on the boundary condition while spurious eigenvalues are different in the different approach, single-layer or double-layer potential MFS. Two examples of circular and elliptical membranes are numerically demonstrated to see the validity of the present method and the results are compared well with the theoretical prediction.

METHOD OF FUNDAMENTAL SOLUTION FOR AN INVERSE HEAT CONDUCTION PROBLEM WITH VARIABLE COEFFICIENTS

2013 ◽  
Vol 10 (02) ◽  
pp. 1341009 ◽  
Author(s):  
MING LI ◽  
XIANG-TUAN XIONG ◽  
YAN LI
Keyword(s):  
Heat Conduction ◽  
Heat Conduction Problem ◽  
Fundamental Solutions ◽  
Variable Coefficients ◽  
Inverse Heat Conduction Problem ◽  
Method Of Fundamental Solutions ◽  
Inverse Heat Conduction ◽  
Modified Method ◽  
On Line ◽  
Ill Posed

In this paper, we consider an inverse heat conduction problem with variable coefficient a(t). In many practical situations such as an on-line testing, we cannot know the initial condition for example because we have to estimate the problem for the heat process which was already started. Based on the method of fundamental solutions, we give a numerical scheme for solving the reconstruction problem. Since the governing equation contains variable coefficients, modified method of fundamental solutions was used to solve this kind of ill-posed problems. Some numerical examples are given for verifying the efficiency and accuracy of the presented method.

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