Rapid Parallel Evaluation of Integrals in Potential Theory on General Three Dimensional Regions

1996 ◽  
pp. 115-125
Author(s):  
Anne Greenbaum ◽  
Anita Mayo ◽  
V. Sonnad
Keyword(s):  
Potential Theory ◽  
Three Dimensional ◽  
Parallel Evaluation

Linear potential theory of steady internal supersonic flow with quasi-cylindrical geometry. Part 1. Flow in ducts

1994 ◽  
Vol 281 ◽  
pp. 159-191 ◽  
Author(s):  
Andreas Dillmann
Keyword(s):  
Supersonic Flow ◽  
Potential Theory ◽  
Broad Class ◽  
Three Dimensional ◽  
Double Series ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Linear Potential ◽  
Linear Potential Theory ◽  
Initial Boundary Value

Based on linear potential theory, the general three-dimensional problem of steady supersonic flow inside quasi-cylindrical ducts is formulated as an initial-boundary-value problem for the wave equation, whose general solution arises as an infinite double series of the Fourier–Bessel type. For a broad class of solutions including the general axisymmetric case, it is shown that the presence of a discontinuity in wall slope leads to a periodic singularity pattern associated with non-uniform convergence of the corresponding series solutions, which thus are unsuitable for direct numerical computation. This practical difficulty is overcome by extending a classical analytical method, viz. Kummer's series transformation. A variety of elementary flow fields is presented, whose complex cellular structure can be qualitatively explained by asymptotic laws governing the propagation of small perturbations on characteristic surfaces.

scholarly journals Some spectral properties of an integral operator in potential theory

1986 ◽  
Vol 29 (3) ◽  
pp. 405-411 ◽  
Author(s):  
John F. Ahner
Keyword(s):  
Potential Theory ◽  
Spectral Properties ◽  
Three Dimensional ◽  
Single Layer ◽  
Integral Operators ◽  
Normal Derivative ◽  
Potential Operator ◽  
Single Layer Potential ◽  
Layer Potential ◽  
Integral Equation Methods

In [7] Plemelj established some fundamental results in two- and three-dimensional potential theory about the eigenvalues of both the double layer potential operator and its adjoint, the normal derivative of the single layer potential operator. In [3] Blumenfeld and Mayer established some additional results concerning the eigenvalues of these integral operators in the case of ℝ2. The spectral properties established by Plemelj [7] and by Blumenfeld and Mayer [3] have had a profound effect in the area of integral equation methods in scattering and potential theory in both ℝ2 and ℝ3.

Variational approach to three-dimensional inverse problems of potential theory

1997 ◽  
Vol 42 (10) ◽  
pp. 1121-1127 ◽  
Author(s):  
É. L. Amromin ◽  
V. A. Bushkovskii
Keyword(s):  
Inverse Problems ◽  
Potential Theory ◽  
Variational Approach ◽  
Three Dimensional

Numerical Sloshing Analysis of FLNG and LNGC Considering Two-Body Motion Effect

2011 ◽  
Author(s):  
Jong Jin Park ◽  
Hiroshi Kawabe ◽  
Mun Sung Kim ◽  
Byung Woo Kim ◽  
Jae Kwang Eom
Keyword(s):  
Numerical Model ◽  
Frequency Domain ◽  
Potential Theory ◽  
Three Dimensional ◽  
Coupled Model ◽  
Ship Motion ◽  
Body Motion ◽  
Liquid Motion ◽  
Motion Effect

Side by Side arrangement is considered for the LNG-FPSO offloading operations. In that case, two-body coupled effects are important for LNG-FPSO and LNGC motion and sloshing analysis. The present study is concerned with a ship motion and sloshing analysis considering two-body motion and sloshing-motion coupled effects. The methodology is based on three-dimensional potential theory on a coupled model of LNG-FPSO and LNGC in the frequency domain. To calculation sloshing impact pressures, the violent liquid motion inside tank is treated with three-dimensional numerical model adopting SOLA-VOF scheme.

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