xx EllSOR

EllSOR

Joan Masso

Date

Abstract

EllSOR provides 3D elliptic solvers for the various classes of elliptic problems defined in EllBase. EllSOR is based on the successive over relaxation algorithm. It is called by the interfaces provided in

EllBase.

1 Purpose

The purpose of this thorn is to provide a simple and straightforward 3D elliptic solver: not to be used by production but to demonstrate key features of the elliptic infrastructure.

This thorn provides

No Pizza No Wine

peace

2 Technical Details

This thorn supports three elliptic problem classes: LinFlat for a standard 3D cartesian Laplace operator, using the standard 7-point computational molecule. LinMetric for a Laplace operator derived from the metric, using 19-point stencil. LinConfMetric for a Laplace operator derived from the metric and a conformal factor, using a 19-point stencil. The code of the solvers differs for the classes and is explained in the following section.

In general, a stencil variable needs to be set for each of the direction relative to the central gridpoint. These

variables are called ac, ae, aw, an, as, at, ab, ane, anw, ase, asw, ate, atw, abe, abw, atn, ats,

abn, asb, where “ac” = a-central, “t” = top, “b” = bottom, “n,s,w,e” = north, south, west, east

2.1 LinFlat

For this class we employ the the 7-point stencil based on at,ab, aw, ae, an, as only. These values are constant at each gridpoint.

2.2 LinMetric

For this class the standard 19-point stencil is initialized, taken the underlying metric into account. The values for the stencil function differ at each gridpoints.

2.3 LinConfMetric

For this class the standard 19-point stencil is initialized, taken the underlying metric and its conformal factor into account. The values for the stencil function differ at each gridpoints.

3 Comments

The sizes of the arrays Mlinear for the coefficient matrix and Nsource are passed in the solver. A storage flag is set if these variables are of a sized greater 1. In this case, the array can be accessed.

4 Parameters

11 ellipticxverbose10 Scope: shared from ELLBASE01KEYWORD

11

5 Interfaces

General Implements: ellsor

Inherits: ellbase boundary

Uses header: EllBase.h EllxDBstructure.h Boundary.h Symmetry.h

6 Schedule This section lists all the variables which are assigned storage by thorn CactusElliptic/EllSOR. Storage can either last for the duration of the run (Always means that if this thorn is activated storage will be assigned, Conditional means that if this thorn is activated storage will be assigned for the duration of the run if some condition is met), or can be turned on for the duration of a schedule function.

Storage NONE

Scheduled Functions

CCTKxBASEGRID x ellsorxregister x register the sor solvers x

11 x 11 Language: 11 c
11 x 11 Type:  11 function