TY - JOUR
T1 - Fast direct solvers for integral equations in complex three-dimensional domains
AU - Greengard, Leslie
AU - Gueyffier, Denis
AU - Martinsson, Per Gunnar
AU - Rokhlin, Vladimir
PY - 2009/5
Y1 - 2009/5
N2 - Methods for the solution of boundary integral equations have changed significantly during the last two decades. This is due, in part, to improvements in computer hardware, but more importantly, to the development of fast algorithms which scale linearly or nearly linearly with the number of degrees of freedom required. These methods are typically iterative, based on coupling fast matrix-vector multiplication routines with conjugate-gradient-type schemes. Here, we discuss methods that are currently under development for the fast, direct solution of boundary integral equations in three dimensions. After reviewing the mathematical foundations of such schemes, we illustrate their performance with some numerical examples, and discuss the potential impact of the overall approach in a variety of settings.
AB - Methods for the solution of boundary integral equations have changed significantly during the last two decades. This is due, in part, to improvements in computer hardware, but more importantly, to the development of fast algorithms which scale linearly or nearly linearly with the number of degrees of freedom required. These methods are typically iterative, based on coupling fast matrix-vector multiplication routines with conjugate-gradient-type schemes. Here, we discuss methods that are currently under development for the fast, direct solution of boundary integral equations in three dimensions. After reviewing the mathematical foundations of such schemes, we illustrate their performance with some numerical examples, and discuss the potential impact of the overall approach in a variety of settings.
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U2 - 10.1017/S0962492906410011
DO - 10.1017/S0962492906410011
M3 - Article
AN - SCOPUS:77949624887
SN - 0962-4929
VL - 18
SP - 243
EP - 275
JO - Acta Numerica
JF - Acta Numerica
ER -