Circular grid solution for Laplace's equation in two dimensions

1973 ◽  
Vol 61 (2) ◽  
pp. 238-239
Author(s):  
R.D. Findlay ◽  
W. Smith
Keyword(s):  
Two Dimensions ◽  
Laplace’S Equation ◽  
Laplace's Equation ◽  
Grid Solution ◽  
Circular Grid

On: “Method of Computing Residual Anomalies from Bouguer Gravity Map by Applying Relaxation Technique” by M. K. Paul (GEOPHYSICS, August 1967, p. 708–719)

Geophysics ◽  
1970 ◽  
Vol 35 (1) ◽  
pp. 160-161
Author(s):  
N. F. Uren
Keyword(s):  
Gravity Field ◽  
Theoretical Basis ◽  
Two Dimensions ◽  
Relaxation Technique ◽  
Bouguer Gravity ◽  
Laplace’S Equation ◽  
Laplace's Equation ◽  
Regional Gravity ◽  
Gravity Map

Dr. M. K. Paul suggests that further investigation of this method may be necessary. The theoretical basis for this method is that [Formula: see text] i.e., that the regional gravity field obeys Laplace’s equation in two dimensions over the plane of observation.

An alǵebraic technique for the solution of Laplace's equation in three dimensions

1970 ◽  
Vol 67 (2) ◽  
pp. 383-389 ◽  
Author(s):  
K. S. Kunz
Keyword(s):  
Conformal Mapping ◽  
Analytic Functions ◽  
Euclidean Plane ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Complex Numbers ◽  
Laplace’S Equation ◽  
Laplace's Equation ◽  
Real Linear ◽  
Algebraic Technique

In obtaining a solution of Laplace's equation in two dimensions by the method of conformal mapping, one first maps the points (x, y) of the Euclidean plane R2 into the algebra of complex numbers C by means of the real-linear function g: R2→C using the prescription g(x, y) = x + iy ≡ z. One then obtains solutions of Laplace's equation by allowing those mappings of C into itself that are expressed by analytic functions.

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