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Geometrically Graded h-p Quadrature Applied to the Complex Boundary Integral Equation Method for the Dirichlet Problem with Corner Singularities [article]

David De Wit
2000 arXiv   pre-print
Traditional boundary integral methods applied to problems with corner singularities involve a (real) boundary integral equation with a kernel containing a logarithmic singularity.  ...  The CBIEM is different in that it involves a complex boundary integral equation with a smooth kernel.  ...  % Kress's Teardrop zn = sin(ptn)*2/sqrt(3) -i * sin(2*ptn); zc = sin(ptc)*2/sqrt(3) -i * sin(2*ptc); gdot = 2*pi*( cos(ptn)/sqrt(3) -i*cos(2*ptn) ); gdot(N) = -2*pi*i; elseif (CCase == 4) % Kress's Boomerang  ... 
arXiv:math/0002189v1 fatcat:pazzaidbdjc3hmhz5crckqtt5m

Approximation and Interpolation [chapter]

Walter Gautschi
2011 Numerical Analysis  
Let be the subdivision D OE0; 1 [ OE1; 2 [ OE2; 3 of the interval [0,3].  ...  We conveniently let the interpolation nodes coincide with the points x i of the subdivision in (2.122). This simplifies matters, but is not necessary (cf. Ex. 75).  ...  2 ; 4/ D 1:764162781524843, .1; 4/ D 0:9816843611112658, . 3 2 ; 4/ D 0:8454501129849537, .2; 4/ D0:9084218055563291, . 5 2 ; 4/ D 1:121650058367554.g Comment on the results. 6. With !  ... 
doi:10.1007/978-0-8176-8259-0_2 fatcat:jjnf7buogrhijg3zuj6q5pohea