Software considerations for the “black box” solver FIDISOL for partial differential equations

Abstract

FIDISOL is a program package for the solution of nonlinear systems of two-dimensional and three-dimensional elliptic and parabolic partial differential equations (PDEs) with nonlinear boundary conditions (BCs) on the boundaries of a rectangular domain. A finite difference method (FDM) with an arbitrary grid and arbitrary consistency order is used, these are either prescribed by the user or are self-adapted for a given relative tolerance. FIDISOL has been designed to be fully vectorizable on vector computers. In this paper we discuss several problems from the viewpoint of software development and user interface, for example, how to deliver the PDEs and BCs to FIDISOL and how to allow a flexible use by a suitable parameter list.

Exploring the Small Mass Limit of Stationary Black Holes in Theories with Gauss-Bonnet Terms

“…The system of coupled PDEs resulting from the EsGB field equations is solved with the FIDISOL/CADSOL solver [71][72][73], which implements a finite difference method together with the root finding Newton-Raphson method. We have also independently developed a new code to verify the accuracy of solutions which utilizes pseudo-spectral methods (and which will be described in a forthcoming publication [74]).…”

Stable Cosmic Vortons

“…The time discretization is achieved using a β-Newmark scheme, which converts (A. 12 a , V [n] are the value of Φ a , V at the time moment t 0 + ndt. Here 0 ≤ β ≤ 1 and the scheme is unconditionally stable for β ≥ 1/4.…”

“…We used three completely different numerical techniques for the vorton construction. First, we performed our calculations using the elliptic PDE solver FIDISOL based on the iterative Newton-Raphson method [12] within a finite difference scheme. This method solves the equations of motion for the stationary, axially symmetric fields.…”

“…Stationary vortons.-Inserting the ansatz (4) to the field equations (3) gives, after separating t and ϕ variables, an elliptic system of 10 non-linear PDE's for the 10 functions of ρ, z. We solve these equations with two different numerical methods: using the elliptic PDE solver FIDISOL based on the Newton-Raphson procedure [12], and also minimizing the energy within a finite element approach provided by the Freefem++ library [13].…”

Solution functions of PDEQSOL (Partial differential EQuation SOlver language) for fluid problems

“…[1][2][3][4] The processing flow of PDEQSOL is shown in figure 1, The PDEQSOL translator generates a Fortran 77 code to solve a PDE discretized problem. The graphical output is also available by means of the postproeessor SGRAF.…”