## EllSOR

Joan Masso

$$Date$$

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