By Constantine Pozrikidis
The Finite point procedure in a single measurement. additional purposes in a single size. High-Order and Spectral parts in a single measurement. The Finite point strategy in Dimensions. Quadratic and Spectral parts in Dimensions. functions in Mechanics. Viscous move. Finite and Spectral point equipment in 3 Dimensions. Appendices. References. Index.
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Additional resources for Introduction to Finite and Spectral Element Methods Using MATLAB, Second Edition
21) 10 Finite and Spectral Element Methods Using MATLAB function xe = elm_line3 (x1,x2,n,ratio); %===================================================== % Symmetric discretization of a line segment into a % graded mesh of n elements subtended % between the left end-point x1 % and the right end-point x2 % % n is odd: 1,3,5,... 4 (→ Continued) Function elm line3 performs the symmetric discretization of a line segment into a graded mesh with an odd number of elements. where δi,j is Kronecker’s delta.
0 0 0 0 .. 1 0 0 .. 6 Global square NE × NE diffusion matrix for linear elements, where hi ≡ xi+1 − xi is the ith element size. 6. In the remainder of this text, we refer to D as the global diffusion matrix. , s NE , sNE +1 T . 30) Note that the global diffusion matrix has units of inverse length, whereas the global mass matrix has units of length. 7(b). 2. 26) takes the form − f2 − f1 q0 1 = + h1 (2 s1 + s2 ). 31) The fraction on the left-hand side expresses the forward difference approximation of the slope at the left end, df /dx = −q0 /k at x = 0.
2 Algorithm for assembling the finite element linear system for steady one-dimensional diffusion, D · f = b, in the case of linear elements. 2 Finite element assembly 27 where the vector r on the right-hand side is tridiagonal form a 1 b1 0 . . 0 c 2 a 2 b2 . . 0 0 c 3 a3 . . 0 .. . . . T= . . . 0 0 0 . . aN −2 0 0 0 . . cN −1 0 0 0 ... 0 specified. The matrix T has the 0 0 0 .. 0 0 0 .. 13) where ai , bi , and ci are specified matrix components. Thomas’s algorithm proceeds in two stages.