The method of fundamental solutions for Poisson's equation

1995 ◽  
Vol 16 (3) ◽  
pp. 205-213 ◽  
Author(s):  
Michael A. Golberg
2013 ◽  
Vol 10 (02) ◽  
pp. 1341006 ◽  
Author(s):  
C. S. CHEN ◽  
C.-S. HUANG ◽  
K. H. LIN

The method of fundamental solutions (MFS) has been an effective meshless method for solving homogeneous partial differential equations. Coupled with radial basis functions (RBFs), the MFS has been extended to solve the inhomogeneous problems through the evaluation of the approximate particular solution and homogeneous solution. In this paper, we prove the the approximate solution of the above numerical process for solving 1D Poisson's equation converges in the sense of Lagrange interpolating polynomial using the result of Driscoll and Fornberg [2002].


Author(s):  
I Pérez-Arjona ◽  
L Godinho ◽  
V Espinosa

Abstract The method of fundamental solutions has been applied to evaluate the influence of fish models geometrical features on the target strength (TS) directivity and TS frequency response of swimbladdered fish. Simplified models were considered for two fish species: gilt-head sea bream (Sparus aurata, Linnaeus 1758) and Atlantic salmon (Salmo salar, Linnaeus 1758), and different geometrical details of their morphology were studied, such as backbone presence, and its curvature or the inclusion of vertebrae modulation. Swimbladder shape and tilt, together with the inclusion of backbone (and its realistic curvature) for dorsal measurements were the most important features for proper estimation of mean TS. The estimation of mean TS is considered including the effect of fish tilt, the echosounder frequency, and the fish-to-transducer distance.


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