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. The e-book additionally offers new equipment, similar to the discontinuous Galerkin approach, and new difficulties, reminiscent of the transmission eigenvalue problem. 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
Read Online or Download Finite element methods for eigenvalue problems PDF
Similar number systems books
Booklet via Brezinski, Claude
The fractional Laplacian, also known as the Riesz fractional by-product, describes an strange diffusion approach linked to random tours. The Fractional Laplacian explores purposes of the fractional Laplacian in technological know-how, engineering, and different parts the place long-range interactions and conceptual or actual particle jumps leading to an abnormal diffusive or conductive flux are encountered.
Additional resources for Finite element methods for eigenvalue problems
Byrne Sinusoids: Theory and Technological Applications, Prem K. Kythe Special Integrals of Gradshteyn and Ryzhik: the Proofs 舑 Volume l, Victor H. Moll Special Integrals of Gradshteyn and Ryzhik: the Proofs 舑 Volume ll, Victor H. Moll Stochastic Cauchy Problems in Infinite Dimensions: Generalized and Regularized Solutions, Irina V. Melnikova Submanifolds and Holonomy, Second Edition, Jɒrgen Berndt, Sergio Console, and Carlos Enrique Olmos The Truth Value Algebra of Type-2 Fuzzy Sets: Order Convolutions of Functions on the Unit Interval, John Harding, Carol Walker, and Elbert Walker Forthcoming Titles Actions and Invariants of Algebraic Groups, Second Edition, Walter Ferrer Santos and Alvaro Rittatore Analytical Methods for Kolmogorov Equations, Second Edition, Luca Lorenzi Geometric Modeling and Mesh Generation from Scanned Images, Yongjie Zhang Groups, Designs, and Linear Algebra, Donald L.
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.