A naturally parallelizable computational method for inhomogeneous parabolic problems
نویسندگان
چکیده
A parallel numerical algorithm is introduced and analyzed for solving inhomogeneous initial-boundary value parabolic problems. The scheme is based on the method recently introduced in [8] for homogeneous problems. We give a method based on a suitable choice of multiple parameters. Our scheme allows to compute solutions in a wide range of time. Instead of using standard time-marching method, which is not easily parallelizable, we take the Laplace transform in time of the parabolic problems. The resulting elliptic problems can be solved in parallel. Solutions are then computed by a discrete inverse Laplace transformation. The parallelization of the algorithm is natural in the sense that it requires no data communication among processors while solving the time-independent elliptic problems. Numerical results are also presented. Subject Classification: 65M12, 65M15, 65M99.
منابع مشابه
A Frequency{domain Method for Finite Element Solutions of Parabolic Problems
We introduce and analyze a frequency-domain method for par-abolic partial diierential equations. The method is naturally parallelizable. After taking the Fourier transformation of given sources in the space-time domain into the space-frequency domain, we propose to solve an indeenite, complex elliptic problem for each frequency. Fourier inversion will then recover the solution in the space-time...
متن کاملHigh Order Smoothing Schemes for Inhomogeneous Parabolic Problems with Applications in Option Pricing
A new family of numerical schemes for inhomogeneous parabolic partial differential equations is developed utilizing diagonal Padé schemes combined with positivity–preserving Padé schemes as damping devices. We also develop a split version of the algorithm using partial fraction decomposition to address difficulties with accuracy and computational efficiency in solving and to implement the algor...
متن کاملVARIATIONAL DISCRETIZATION AND MIXED METHODS FOR SEMILINEAR PARABOLIC OPTIMAL CONTROL PROBLEMS WITH INTEGRAL CONSTRAINT
The aim of this work is to investigate the variational discretization and mixed finite element methods for optimal control problem governed by semi linear parabolic equations with integral constraint. The state and co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control is not discreted. Optimal error estimates in L2 are established for the state...
متن کاملکاربرد روش معادله سهموی در تحلیل مسائل انتشار امواج داخل ساختمان
With the rapid growth of indoor wireless communication systems, the need to accurately model radio wave propagation inside the building environments has increased. Many site-specific methods have been proposed for modeling indoor radio channels. Among these methods, the ray tracing algorithm and the finite-difference time domain (FDTD) method are the most popular ones. The ray tracing approach ...
متن کامل