Jiguang Sun, Aihui Zhou's Finite element methods for eigenvalue problems PDF

By Jiguang Sun, Aihui Zhou

This ebook covers finite point equipment for numerous common eigenvalues that come up from technological know-how and engineering. either concept and implementation are coated intensive on the graduate point. The history for general eigenvalue difficulties is incorporated besides useful research instruments, finite aspect discretization equipment, convergence research, suggestions for matrix evaluate difficulties, and computing device implementation. Read more...

summary: This publication covers finite aspect tools for numerous commonplace eigenvalues that come up from technology and engineering. either thought and implementation are lined intensive on the graduate point. The history for general eigenvalue difficulties is integrated in addition to useful research instruments, finite aspect discretization equipment, convergence research, concepts for matrix assessment difficulties, and desktop implementation. The ebook additionally provides new equipment, corresponding to the discontinuous Galerkin technique, and new difficulties, corresponding to the transmission eigenvalue challenge

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This is a fourth order problem. The study of finite element methods for it has barely started. Chapter 6 is on the transmission eigenvalue problem, a new research topic arising from the inverse scattering theory. The problem is extremely challenging since it is nonlinear and nonself-adjoint. Only very recently, the problem drew some attention of numerical analysts. In fact, the theory of the problem is not complete yet. We present several methods including iterative methods and two mixed methods.

15. Let X be a vector space over the complex numbers 葐. An inner product on X is a mapping (ƃ, ƃ)X : X ȕ X 薔 葐 such that (1) (x, x)X 蠅 0, (x, x)X = 0 if and only if x = 0; (2) (x,y)¯X = (y, x)X for all x, y 蜒 X; (3) for all x, y, z 蜒 X and ॅ, ॆ 蜒 葐 we have that (ॅx + ॆy, z)X = ॅ(x, z)X + ॆ(y, z)X. For simplicity, we write an inner product on X as (ƃ, ƃ) when there is no confusion from context. Sometimes we refer to inner product as scalar product. The inner product induces a norm on X: 舔x舔X=(x,x)Xfor all舁x蜒X.

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