A method of fundamental solutions for heat and wave propagation from lateral Cauchy data

2021 ◽  
Author(s):  
Ihor Borachok ◽  
Roman Chapko ◽  
B. Tomas Johansson
Keyword(s):  
Wave Propagation ◽  
Fundamental Solutions ◽  
Cauchy Data ◽  
Method Of Fundamental Solutions

A Moving Pseudo-Boundary MFS for Three-Dimensional Void Detection

2013 ◽  
Vol 5 (04) ◽  
pp. 510-527 ◽  
Author(s):  
Andreas Karageorghis ◽  
Daniel Lesnic ◽  
Liviu Marin
Keyword(s):  
Three Dimensional ◽  
Nonlinear Least Squares ◽  
Fundamental Solutions ◽  
Cauchy Data ◽  
Three Dimensions ◽  
Method Of Fundamental Solutions ◽  
Void Detection ◽  
Spherical Parametrization ◽  
Least Squares Minimization

AbstractWe propose a new moving pseudo-boundary method of fundamental solutions (MFS) for the determination of the boundary of a three-dimensional void (rigid inclusion or cavity) within a conducting homogeneous host medium from overdetermined Cauchy data on the accessible exterior boundary. The algorithm for imaging the interior of the medium also makes use of radial spherical parametrization of the unknown star-shaped void and its centre in three dimensions. We also include the contraction and dilation factors in selecting the fictitious surfaces where the MFS sources are to be positioned in the set of unknowns in the resulting regularized nonlinear least-squares minimization. The feasibility of this new method is illustrated in several numerical examples.

scholarly journals Coupling the BEM/TBEM and the MFS for the Numerical Simulation of Wave Propagation in Heterogeneous Fluid-Solid Media

2011 ◽  
Vol 2011 ◽  
pp. 1-26 ◽  
Author(s):  
António Tadeu ◽  
Igor Castro
Keyword(s):  
Wave Propagation ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Transient Analysis ◽  
Fundamental Solutions ◽  
Method Of Fundamental Solutions ◽  
Cpu Time ◽  
Solid Media ◽  
Full Domain ◽  
Element Method

This paper simulates wave propagation in an elastic medium containing elastic, fluid, rigid, and empty heterogeneities, which may be thin. It uses a coupling formulation between the boundary element method (BEM)/the traction boundary element method (TBEM) and the method of fundamental solutions (MFS). The full domain is divided into subdomains, which are handled separately by the BEM/TBEM or the MFS, to overcome the specific limitations of each of these methods. The coupling is enforced by applying the prescribed boundary conditions at all medium interfaces. The accuracy, efficiency, and stability of the proposed algorithms are verified by comparing the results with reference solutions. The paper illustrates the computational efficiency of the proposed coupling formulation by computing the CPU time and the error. The transient analysis of wave propagation in the presence of a borehole driven in a cracked medium is used to illustrate the potential of the proposed coupling formulation.

PREDICTION OF ACOUSTIC WAVE PROPAGATION IN A SHALLOW WATER CONFIGURATION USING THE METHOD OF FUNDAMENTAL SOLUTIONS

2012 ◽  
Vol 20 (04) ◽  
pp. 1250013 ◽  
Author(s):  
E. G. A. COSTA ◽  
L. GODINHO ◽  
A. PEREIRA ◽  
J. A. F. SANTIAGO
Keyword(s):  
Wave Propagation ◽  
Acoustic Wave ◽  
Shallow Water ◽  
Free Water ◽  
Numerical Approach ◽  
Fundamental Solutions ◽  
Method Of Fundamental Solutions ◽  
Acoustic Wave Propagation ◽  
Water Region ◽  
Shallow Water Region

An efficient and accurate numerical frequency domain formulation is proposed to investigate the 2D acoustic wave propagation within a shallow water region with a rigid bottom and a free surface. The proposed configuration combines different regions that have either a sloping or a flat rigid bottom. The numerical approach used here is based on the method of fundamental solutions (MFS). In this model only the vertical interface between different regions is discretized, as the model incorporates Green's functions that take into account the free water surface and the presence of either a horizontal or sloping rigid bottom.

scholarly journals Influence of fish backbone model geometrical features on the numerical target strength of swimbladdered fish

2020 ◽  
Author(s):  
I Pérez-Arjona ◽  
L Godinho ◽  
V Espinosa
Keyword(s):  
Atlantic Salmon ◽  
Salmo Salar ◽  
Sparus Aurata ◽  
Fundamental Solutions ◽  
Sea Bream ◽  
Method Of Fundamental Solutions ◽  
Target Strength ◽  
Simplified Models ◽  
Geometrical Features ◽  
Proper Estimation

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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