Index

NAME

FieldWithPtValues - base class for fields having point values

INCLUDE

include "FieldWithPtValues.h"

SYNTAX

 class FieldWithPtValues : public Field
 {
 protected:
   FieldWithPtValues (const char* name = NULL) : Field(name) {}

 public:
  ~FieldWithPtValues () {}

   virtual NUMT& valuePoint (int point_no) =0;
   virtual NUMT  valuePoint (int point_no) const =0;
   virtual Ptv(real) getPt (int point_no) const =0;
   virtual int getNoPoints () const =0;
   virtual int getNoValues () const =0;
   virtual GridWithPts& getGridWithPts () =0;
   virtual const GridWithPts& getGridWithPts () const =0;
   virtual Vec(NUMT)& valuesVec () =0;
   virtual const Vec(NUMT)& valuesVec () const =0;

   CLASS_INFO

   VIRTUAL_CAST(FieldWithPtValues)
 };

KEYWORDS

scalar field, base class, point values

DESCRIPTION

The  class serves as base class for all field classes where it is
meaningful to consider the  field  as  a  grid,  containing  grid
points,  and  an  array with the field values at the grid points.
Most fields used for numerical computations  are  of  this  type.
However,  there are important exceptions. Galerkin or collocation
methods utilizing global test and trial functions  (for  example,
sine/cosine)  give  rise  to  a field abstraction where the basis
functions can be viewed as the grid and the coefficients  in  the
expansion is naturally collected in an array. However, this array
does not reflect the field values at grid points.

The purpose of the class is to offer a unified interface to  some
important  field representations. One very convenient application
is the generation of stochastic fields. Most algorithms for  such
problems  are  based  on  manipulating  field  values at discrete
points in space.  Representing the field as  a  FieldWithPtValues
handle  (or  reference or pointer) makes it easy to code an algo­
rithm that applies to finite difference fields over regular  uni­
form  grids  (FieldLattice), scattered point fields (FieldScatPt)
and finite element fields (FieldFE).

CONSTRUCTORS AND INITIALIZATION

There is no data in the class so there is no specific initializa­
tion  requirement.  The only constructor takes no arguments, or a
field name, and has an empty body.

MEMBER FUNCTIONS

valuePoint - returns access to  the  field  value  at  a  spatial
point.   The point is given by its point number. (If the point is
known by its coordinates and not the point number,  one  can  use
the valuePt function, see class Field).

getPt  - returns the coordinate of a point. The point is given by
its point number in the grid.

getNoPoints - returns the number of points in the grid.

getNoValues - returns the number of field values  (usually  equal
to the number of points).In a GridLattice grid one can think of a
finite difference field defined at the  cell  centers.  Then  the
number  of grid points does not coincide with the number of field
values.  However, the field is typically characterized  as  being
defined at a finite number of spatial points.

getGridWithPts  - gives access to the grid object associated with
the FieldWithPtValues object. The corresponding  base  class  for
grid with discrete points is GridWithPts.

SEE ALSO

class Fields

DEVELOPED BY

SINTEF Applied Mathematics, Oslo, Norway, and University of Oslo,
Dept. of Mathematics, Norway

AUTHOR

Hans Petter Langtangen, SINTEF/UiO