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Theorem (One point compactification) Any locally compact space \(X\) can be embedded in another compact space \(Y\), which just has one more point tha 阅读全文
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For a normed space \(X\), an isometric isomorphism can be defined from \(X\) to its second dual space \(X''\), i.e. \(J: X \rightarrow X''\), such tha 阅读全文
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In a computer simulation of the real world, physical quantities, which usually have continuous distributions governed by partial differential equation 阅读全文
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Introduction Among simulation engineers, it is well accepted that the solution of a PDE can be envisioned as the following three general steps (actual 阅读全文
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In functional analysis, several types of convergence are defined, namely, strong convergence for elements in normed linear space. weak convergence for 阅读全文
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This article introduces how to derive the representation formula used in BEM from Green's identity. Interior and exterior representation formulas Let 阅读全文
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In our "last article" , we introduced four integral operators in the boundary integral equations in BEM. Among them, the two compact operators $T_K$ a 阅读全文
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Boundary element method (BEM) is an effective tool compared to finite element method (FEM) for resolving those electromagnetic field problems includin 阅读全文
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In general differential calculus, we have learned the definitions of function continuity, such as functions of class \(C^0\) and \(C^2\). For most cas 阅读全文
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John M. Lee is a famous mathematician, who bears the reputation of writing the classical book "Introduction to Smooth Manifolds". In his article, "Som 阅读全文