New PDF release: Artificial Boundary Method

By Houde Han, Xiaonan Wu

ISBN-10: 3642354637

ISBN-13: 9783642354632

ISBN-10: 3642354645

ISBN-13: 9783642354649

"Artificial Boundary process" systematically introduces the unreal boundary process for the numerical recommendations of partial differential equations in unbounded domain names. certain discussions deal with sorts of difficulties, together with Laplace, Helmholtz, warmth, Schrödinger, and Navier and Stokes equations. either numerical tools and blunder research are mentioned. The publication is meant for researchers operating within the fields of computational arithmetic and mechanical engineering.
Prof. Houde Han works at Tsinghua collage, China; Prof. Xiaonan Wu works at Hong Kong Baptist collage, China.

Show description

Read Online or Download Artificial Boundary Method PDF

Similar counting & numeration books

Download e-book for iPad: Number theory vol.1. Tools and diophantine equations by Henri Cohen

The crucial subject is the answer of Diophantine equations, i. e. , equations or platforms of polynomial equations which has to be solved in integers, rational numbers or extra normally in algebraic numbers. This topic, particularly, is the significant motivation for the fashionable conception of mathematics algebraic geometry.

Download PDF by Alla Borisyuk, G. Bard Ermentrout, Avner Friedman, David H.: Tutorials in Mathematical Biosciences I: Mathematical

This quantity introduces a few uncomplicated theories on computational neuroscience. bankruptcy 1 is a quick creation to neurons, adapted to the following chapters. bankruptcy 2 is a self-contained creation to dynamical structures and bifurcation concept, orientated in the direction of neuronal dynamics. the speculation is illustrated with a version of Parkinson's disorder.

Download PDF by Tom Lyche, Jean-Louis Merrien (auth.): Exercises in Computational Mathematics with MATLAB

Designed to supply instruments for autonomous research, this e-book comprises student-tested mathematical routines joined with MATLAB programming workouts. such a lot chapters open with a assessment by means of theoretical and programming workouts, with certain recommendations supplied for all difficulties together with courses.

Additional resources for Artificial Boundary Method

Sample text

30) has a unique solution uN (x) ∈ H 1 (Ωi ). 30), respectively, and C > 0 is a constant not depending on N . Proof. Let a( N (x) = u(x) − uN (x). Then, N , v) + bN ( N N (x) ∈ V0 and satisfies , v) = bN (u, v) − b(u, v), ∀v ∈ V0 . 2, we obtain N 2 1,Ωi α , N ) + bN ( = bN (u, N ) − b(u, a( N N , N N ) ). 3) of the 3-D Poisson equation. For r R0 , u(x) satisfies the Laplace equation. Expand u(R0 , θ, ϕ) in an infinite series as follows: ∞ u(R0 , θ, ϕ) = an0 0 a00 + P (cos θ) 2 2 n n=1 n Pnm (cos θ)(anm cos mϕ + bnm sin mϕ) .

BR On BR , we consider the following boundary value problem: Δv ∗ (x) = 0, ∀x ∈ BR , v ∗ (x) = v(x), ∀x ∈ ΓR . 60) has a unique solution and |∇v ∗ |2 dx |∇˜ v |2 dx = BR BR Ωi |∇v|2 dx. 58) of v on ΓR , we obtain the following series form for v ∗ : v ∗ (r, θ) = ∞ r c0 + 2 R n=1 n (cn cos nθ + dn sin nθ). 61), we obtain |∇v ∗ |2 dx = BR 2π ∂v ∗ ∂r R 0 ∞ 0 2π R = n=1 0 0 ∞ R = 2π n=1 ∞ =π 0 + r−2 ∂v ∗ ∂θ 2 rdrdθ n2 r2n−2 2 (cn + d2n )rdrdθ R2n n2 r2n−1 2 (cn + d2n )dr R2n n(c2n + d2n ) n=1 2 = π|v ∗ |1/2,ΓR 24 2 2 = π|v|1/2,ΓR .

59), we obtain |a(v − u, v − uN,R ) + bN (v − u, v − uN,R )| h h 2|v − u|1,Ωi v − uN,R h 1,Ω . 67), we find v−uN,R h 1,Ωi R0 1 (N +1)k−1 R N +1 |u|k−1/2,Γ0 +2|v−u|1,Ωi , ∀v ∈ V0h . 68) Finally, using the triangle inequality, we get the following estimate: 25 Artificial Boundary Method u−uN,R h 1,Ωi |u − v|1,Ωi + v − uN,R h R0 1 (N +1)k−1 R N +1 1,Ωi |u|k−1/2,Γ0 +3|u−v|1,Ωi , ∀v ∈ V0h . 63) holds. 63), we see clearly how the error u−uN,R is dependent h on the finite element mesh size (h), the accuracy of the artificial boundary (N ), and the position of the artificial boundary (R).

Download PDF sample

Artificial Boundary Method by Houde Han, Xiaonan Wu


by Michael
4.5

Rated 4.21 of 5 – based on 19 votes