Download Fast Algorithms and Their Applications to Numerical by Daoud Sulaiman Mashat PDF

By Daoud Sulaiman Mashat

A numerical strategy for quasiconformal mapping of doubly hooked up domain names onto
annuli is gifted. The annulus itself isn't really identified a priori and is decided as
part of the answer strategy. The numerical approach calls for fixing a sequence
of inhomogeneous Beltrami equations, each one inside of a unique annulus, in an iterative
mode. The annulus during which the equation is being solved can be updated
during the iterations utilizing an updating strategy in response to the bisection method.
This quasiconformal mapping technique relies on Daripa's approach to quasiconformal
mapping of easily hooked up domain names onto unit disks. The functionality of
the quasiconformal mapping set of rules has been proven on a number of doubly
connected domain names with varied complicated dilations.
The answer of the Beltrami equation in an annulus calls for comparing two
singular vital operators. speedy algorithms for his or her exact evaluate are presented.
These are in response to extension of a quick set of rules of Daripa. those algorithms
are in keeping with a few recursive family members in Fourier house and the FFT (fast
Fourier transform), and feature theoretical computational complexity of order log N
per aspect.

Show description

Read Online or Download Fast Algorithms and Their Applications to Numerical Quasiconformal Mappings of Doubly Connected Domains Onto Annuli PDF

Similar computational mathematicsematics books

Hybrid Systems: Computation and Control: Third International Workshop, HSCC 2000 Pittsburgh, PA, USA, March 23–25, 2000 Proceedings

This ebook constitutes the refereed complaints of the 3rd foreign Workshop on Hybrid platforms: Computation and regulate, HSCC 2000, held in Pittsburgh, PA, united states in March 2000. The 32 revised complete papers offered including abstracts of 4 invited talks have been conscientiously reviewed and chosen from a complete of seventy one papers submitted.

Finite Element Method: A Practical Course

The Finite point procedure (FEM) has develop into an fundamental expertise for the modelling and simulation of engineering structures. Written for engineers and scholars alike, the purpose of the publication is to supply the required theories and methods of the FEM for readers so one can use a advertisement FEM package deal to unravel basically linear difficulties in mechanical and civil engineering with the focus on structural mechanics and warmth move.

Biological Magnetic Resonance - Volume 17: Structural Computation and Dynamics in Protein (Biological Magnetic Resonance)

Quantity 17 of organic Magnetic Resonance (Structure Computation and Dynamics) represents major advances in the biomolecular NMR box, with emphasis on advancements in the course of the fresh years. This e-book brings jointly many of the world's most popular specialists who've supplied huge management in advancing the sector.

Computational Logic in Multi-Agent Systems: 11th International Workshop, CLIMA XI, Lisbon, Portugal, August 16-17, 2010, Proceedings

This e-book constitutes the lawsuits of the eleventh overseas Workshop on Computational common sense in Multi-Agent structures, CLIMA XI, held in Lisbon, Portugal, in August 2010. The 14 papers offered have been conscientiously reviewed and chosen from 31 submissions. additionally four invited talks are provided. the aim of the CLIMA workshops is to supply a discussion board for discussing concepts, according to computational good judgment, for representing, programming and reasoning approximately brokers and multi-agent platforms in a proper means.

Additional resources for Fast Algorithms and Their Applications to Numerical Quasiconformal Mappings of Doubly Connected Domains Onto Annuli

Example text

C_ 1 (r1) = 2, then set Bs,2(rl) = hs+2(rr) for l E [2, M) and s E Step 8. For l E (1, M) and s E [-Q, Q- m). Set Ss,m(rt) Step 9. OUTPUT Tmh(a = ne 2 rrik/N) [-Q, Q- 2). = Bs,m(rl) + Cs,m(rr). ::: Ss,m(rt)e 2rriks/N. s=-Q STOP. 1. N must be a power of two. 2. Q must be greater than 2. 2. The Algorithmic Complexity We consider the computational complexity of the above algorithm. Below We discuss the asymptotic operation count and asymptotic storage requirement. A brief analysis of the algorithmic complexity follows.

Step 4. Compute Cs,m(rz) for s E {[-Q, -m] U [0, Q -m]} and l E [1, M] as follows: Set Cs,M(rM) = 0 for all s E [0, Q- m] do l = M - 1, ... , 1 19 end do Set Cs,m(rl) = 0 for all s E [-Q, -m) dol= 2, ... ,M end do = 2, then set If m = 1, then set Step 5. If m Step 6. Step 7. If m = 0 for l E [1, M). Bs,I(rt) = 0, s E [-Q, Q- 1). C_ 1 (r1) = 2, then set Bs,2(rl) = hs+2(rr) for l E [2, M) and s E Step 8. For l E (1, M) and s E [-Q, Q- m). Set Ss,m(rt) Step 9. OUTPUT Tmh(a = ne 2 rrik/N) [-Q, Q- 2).

33 TABLE 3 Comparison of the inner radius of the annulus when N = 256 for the domain in Example 12 with ). = ). 27 X X 10- 4 10- 4 Iteration I 17 16 16 Iteration II 15 15 15 TABLE 4 Comparison of the inner radius of the annulus when M = 51 for the domain in Example 12 with ). = ). 01355 Iteration I 17 10 9 Iteration II 15 15 15 34 Figure 3. Quasiconformal mapprng of the illterior of the annulus onto the illterior of the doubly connected domarn G for Example 1. 0 Figure 4. Convergence of F(Ro) for Example 1.

Download PDF sample

Rated 4.09 of 5 – based on 5 votes