Graphing capabilities for CHIEF (combined Helmholtz integral equation formulation)

1990 ◽  
Vol 88 (S1) ◽  
pp. S137-S137
Author(s):  
C. M. Siders
Keyword(s):  
Integral Equation ◽  
Equation Formulation ◽  
Integral Equation Formulation ◽  
Helmholtz Integral

BOUNDARY ELEMENT SOLUTION OF A BODY'S EXTERIOR ACOUSTIC FIELD NEAR ITS INTERNAL EIGENVALUES

1993 ◽  
Vol 01 (03) ◽  
pp. 335-353 ◽  
Author(s):  
R. A. MARSCHALL
Keyword(s):  
Integral Equation ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Singular Value ◽  
Practical Implementation ◽  
Equation Formulation ◽  
Integral Equation Formulation ◽  
Value Decomposition ◽  
Element Method ◽  
Helmholtz Integral

A relatively straightforward Boundary Element Method (BEM) for the numerical solution of the exterior Helmholtz problem is specified in a tutorial fashion. The algorithm employs the Combined Helmholtz Integral Equation Formulation (CHIEF) and then Singular Value Decomposition (SVD) to solve the resulting system. Its accuracy and convergence characteristics are examined, and compared to the simplest boundary element method for exterior acoustics, the Helmholtz Integral Equation Formulation or HIEF. Boundary element and auxiliary (CHIEF) point requirements to obtain BEM solutions of a desired accuracy are described. This particular CHIEF algorithm is found to largely avoid the numerical difficulties of the HIEF technique while retaining theoretical and practical implementation simplicity.

On periodic water-waves and their convergence to solitary waves in the long-wave limit

1981 ◽  
Vol 303 (1481) ◽  
pp. 633-669 ◽  
Keyword(s):  
Integral Equation ◽  
Solitary Waves ◽  
Water Waves ◽  
Periodic Problem ◽  
Existence Theory ◽  
Periodic Waves ◽  
Equation Formulation ◽  
Long Wave ◽  
Integral Equation Formulation ◽  
Wave Limit

A detailed discussion of Nekrasov’s approach to the steady water-wave problems leads to a new integral equation formulation of the periodic problem. This development allows the adaptation of the methods of Amick & Toland (1981) to show the convergence of periodic waves to solitary waves in the long-wave limit. In addition, it is shown how the classical integral equation formulation due to Nekrasov leads, via the Maximum Principle, to new results about qualitative features of periodic waves for which there has long been a global existence theory (Krasovskii 1961, Keady & Norbury 1978).

An integral equation formulation for the unconfined flow of groundwater with variable inlet conditions

1995 ◽  
Vol 18 (1) ◽  
pp. 15-36 ◽  
Author(s):  
Z. -X. Chen ◽  
G. S. Bodvarsson ◽  
P. A. Witherspoon ◽  
Y. C. Yortsos
Keyword(s):  
Integral Equation ◽  
Equation Formulation ◽  
Unconfined Flow ◽  
Integral Equation Formulation ◽  
Inlet Conditions
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