On the Numerical Solution of Helmholtzs Equation By the Capacitance Matrix Meth
On the Numerical Solution of Helmholtzs Equation By the Capacitance Matrix Meth
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Dianne P. O'Leary and the second author are exploring the exten- sion of a variant of our method to three dimensions.
Acknowledgements . The authors want to thank J. Cooley for pro- viding us with a fine fast Fourier transform program and C. Paige and M. Saunders for an excellent conjugate gradient routine. The authors also want to thank P. Concus, G. Dahlquist, A. George, G. Golub, 0. Hald, H. 0. Kreiss, D. Martin, S. Osher, C. Peskin, V. Pereyra and A. Shieh for their interest and encourageme...nt.
2. Certain results from classical potential theory We give only a brief review of a few results of potential theory. For a detailed exposition see the references given in the previous section. We begin by defining the potential ^ resulting from a charge distribution p on a boundary curve do, Y(x) = (l/ir)/ pU) log (l/r)dsU) . DO We will assume throughout that the boundary dO is sufficiently 2 2 2 smooth. Here x = (x 1, x 2 ), i = (i 1, i 2 ^ and r = ( x l~^l^ + ( x 2 ~^2^ ' We note that (l/2rr) log ( 1/r ) is a fundamental solution of Poisson's equation, i.
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To quickly assess the difficulty of the text, read a short excerpt:
Dianne P. O'Leary and the second author are exploring the exten- sion of a variant of our method to three dimensions.
Acknowledgements . The authors want to thank J. Cooley for pro- viding us with a fine fast Fourier transform program and C. Paige and M. Saunders for an excellent conjugate gradient routine. The authors also want to thank P. Concus, G. Dahlquist, A. George, G. Golub, 0. Hald, H. 0. Kreiss, D. Martin, S. Osher, C. Peskin, V. Pereyra and A. Shieh for their interest and encourageme...nt.
2. Certain results from classical potential theory We give only a brief review of a few results of potential theory. For a detailed exposition see the references given in the previous section. We begin by defining the potential ^ resulting from a charge distribution p on a boundary curve do, Y(x) = (l/ir)/ pU) log (l/r)dsU) . DO We will assume throughout that the boundary dO is sufficiently 2 2 2 smooth. Here x = (x 1, x 2 ), i = (i 1, i 2 ^ and r = ( x l~^l^ + ( x 2 ~^2^ ' We note that (l/2rr) log ( 1/r ) is a fundamental solution of Poisson's equation, i.
What to read after On the Numerical Solution of Helmholtzs Equation By the Capacitance Matrix Meth?
You can find similar books in the "Read Also" column, or choose other free books by Olof B Widlund to read onlineMoreLess
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