The following information was submitted:
Transactions: INTERNATIONAL JOURNAL of APPLIED MATHEMATICS AND INFORMATICS
Transactions ID Number: 19-123
Full Name: Chrysovalantis Sfyrakis
Position: Assistant Professor
Age: ON
Sex: Male
Address: Marikas Kottopouli 22, Neo Herakleio - Attiki
Country: GREECE
Tel: +302102796983
Tel prefix: +306937050504
Fax: +302102796983
E-mail address: hammer@math.uoa.gr
Other E-mails: sfyrakis@gmail.com
Title of the Paper: Parallel Finite Difference Methods for phase change problems in materials
Authors as they appear in the Paper: Chr. A. Sfyrakis
Email addresses of all the authors: hammer@math.uoa.gr
Number of paper pages: 9
Abstract: The great complexity of the problems in phase change materials to us to develop from a fast and methods to solve with parallel programming techniques. We consider the phase field model consisting of the system of p.d.e' s $$\left. \begin{tabular}{l} $\displaystyle{q(\theta)\phi_t=\nabla\cdot\left(A(\theta)\nabla \phi\right)+f(\phi,u)},$ \\ $\displaystyle{u_t=\Delta u+\left[p(\phi)\right]_t},$ \\ \end{tabular} \right.$$ where $\phi=\phi(x,y,t)$ is the phase indicator function, $\theta=\arctan(\phi_y/\phi_x)$, $u=u(x,y,t)$ is the temperature, $q,\ p,$ and $f$ are given scalar functions, and $A$ is a $2\times2$ matrix of given functions of $\theta$. This system describes the evolution of phase and temperature in a two-phase medium, and is posed for $t\geq 0$ on a rectangle in the $x,y$ plane with appropriate boundary and initial conditions. We solve the system using two finite difference methods. The first method is based on the explicit Euler scheme for the first eq!
uation and the Crank-Nicolson-ADI method for the second. The other method uses for both equations the Crank-Nicolson-ADI scheme. We show results of relevant numerical experiments, compare the errors of the two methods, and compare their speed-up when we implement them using parallel processors. Also make comparisons between the methods as and for each method separately and draw conclusions depending on the number of nodes and the speed of execution method in one, two and four processors.
Keywords: finite difference methods, simplified phase-field models, Parabolic system, explicit Euler scheme, Crank-Nicolson-ADI method, Error estimates, parallel implementation.
EXTENSION of the file: .pdf
Special (Invited) Session: Accelerated Finite Difference Methods for a Simplified Phase Field Model
Organizer of the Session: 615-096
How Did you learn about congress: notaris@math.uoa.gr, mmitroul@math.uoa.gr, doug@math.uoa.gr
IP ADDRESS: 92.119.45.252
