On high accuracy schemes of the method of straight lines for two-dimensional parabolic equations

1997 ◽  
Vol 86 (4) ◽  
pp. 2857-2865
Author(s):  
A. P. Kubanskaya
Keyword(s):  
Parabolic Equations ◽  
High Accuracy ◽  
Two Dimensional ◽  
Method Of Straight Lines ◽  
Straight Lines

A High-Accuracy Mechanical Quadrature Method for Solving the Axisymmetric Poisson's Equation

2017 ◽  
Vol 9 (2) ◽  
pp. 393-406 ◽  
Author(s):  
Hu Li ◽  
Jin Huang
Keyword(s):  
Three Dimensional ◽  
High Accuracy ◽  
Poisson’S Equation ◽  
Two Dimensional ◽  
Quadrature Method ◽  
Poisson's Equation ◽  
Mechanical Quadrature ◽  
Asymptotic Error ◽  
Accuracy Order ◽  
Mechanical Quadrature Method

AbstractIn this article, we consider the numerical solution for Poisson's equation in axisymmetric geometry. When the boundary condition and source term are axisymmetric, the problem reduces to solving Poisson's equation in cylindrical coordinates in the two-dimensional (r,z) region of the original three-dimensional domain S. Hence, the original boundary value problem is reduced to a two-dimensional one. To make use of the Mechanical quadrature method (MQM), it is necessary to calculate a particular solution, which can be subtracted off, so that MQM can be used to solve the resulting Laplace problem, which possesses high accuracy order and low computing complexities. Moreover, the multivariate asymptotic error expansion of MQM accompanied with for all mesh widths hi is got. Hence, once discrete equations with coarse meshes are solved in parallel, the higher accuracy order of numerical approximations can be at least by the splitting extrapolation algorithm (SEA). Meanwhile, a posteriori asymptotic error estimate is derived, which can be used to construct self-adaptive algorithms. The numerical examples support our theoretical analysis.

Solution of Stefan's problem by the method of straight lines

1969 ◽  
Vol 9 (3) ◽  
pp. 113-126 ◽  
Author(s):  
R.D. Bachelis ◽  
V.G. Melamed ◽  
D.B. Shlyaifer
Keyword(s):  
Method Of Straight Lines ◽  
Straight Lines

Magnetic Breakdown in a dislocated lattice

1965 ◽  
Vol 287 (1409) ◽  
pp. 165-182 ◽  
Keyword(s):  
Electrical Conductivity ◽  
Random Walk ◽  
Dislocation Density ◽  
Network Model ◽  
Random Phase ◽  
Two Dimensional ◽  
Magnetic Breakdown ◽  
Low Dislocation Density ◽  
Electron Orbit ◽  
Straight Lines

The network model of electron orbits coupled by magnetic breakdown is extended to a two dimensional metal containing dislocations. It is shown that the network is still likely to be a valid representation, but the phase lengths of the arms are altered, and a very low dislocation density (about one per electron orbit) is enough to produce almost complete randomization. The Bloch-like quasi-particles that can travel in straight lines on a perfect network are now heavily scattered, and it is preferable to think of electrons performing a random walk on the arms of the network, although the justification for this procedure is somewhat doubtful. A simpler alternative to Falicov & Sievert’s method is presented for calculating the electrical conductivity of a random-phase network, and is extended to cases where randomness affects only some of the phases, as is believed to be the situation in real metals like zinc and magnesium.

Sign in / Sign up

Export Citation Format

Share Document