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Heritage and early history of the boundary element method. (English) Zbl 1182.65005
Summary: This article explores the rich heritage of the boundary element method (BEM) by examining its mathematical foundation from the potential theory, boundary value problems, Green’s functions, Green’s identities, to Fredholm integral equations. The 18th to 20th century mathematicians, whose contributions were key to the theoretical development, are honored with short biographies. The origin of the numerical implementation of boundary integral equations can be traced to the 1960s, when the electronic computers had become available. The full emergence of the numerical technique known as the boundary element method occurred in the late 1970s. This article reviews the early history of the boundary element method up to the late 1970s.

MSC:
65-03 History of numerical analysis
65N38 Boundary element methods for boundary value problems involving PDEs
65M38 Boundary element methods for initial value and initial-boundary value problems involving PDEs
74S15 Boundary element methods applied to problems in solid mechanics
76M15 Boundary element methods applied to problems in fluid mechanics
01A60 History of mathematics in the 20th century
01A55 History of mathematics in the 19th century
01A50 History of mathematics in the 18th century
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