.TH "problem" 2rheolef "Version 7.2" "rheolef" \" -*- nroff -*-
.ad l
.nh
.SH NAME
problem \- linear solver (rheolef-7\&.2)
.SH "DESCRIPTION"
.PP
The \fCproblem\fP class solves a given linear system for PDEs in variational formulation\&.
.SH "DESCRIPTION"
.PP
The degrees of freedom are splitting between \fIunknown\fP degrees of freedom and \fIblocked\fP one\&. See also \fBform(2)\fP and \fBspace(2)\fP\&. Let \fCa\fP be a bilinear \fBform(2)\fP and \fClh\fP be the right-hand-side, as in the previous example\&. The linear system expands as: 
.PP
.nf
    [ a\&.uu  a\&.ub ] [ uh\&.u ]   [ lh\&.u ]
    [            ] [      ] = [      ]
    [ a\&.bu  a\&.bb ] [ uh\&.b ]   [ lh\&.b ]

.fi
.PP
 The \fCuh\&.b\fP are blocked degrees of freedom: their values are prescribed and the corresponding values are move to the right-hand-side of the system that reduces to: 
.PP
.nf
    a\&.uu*uh\&.u =  lh\&.u - a\&.ub*uh\&.b

.fi
.PP
 This writes: 
.PP
.nf
    problem p (a);
    p\&.solve (lh, uh);

.fi
.PP
 Observe that, during the \fCp\&.solve\fP call, \fCuh\fP is both an input variable, for the \fCuh\&.b\fP contribution to the right-hand-side, and an output variable, with \fCuh\&.u\fP\&. When using an iterative resolution, the details about its convergence, e\&.g\&. the number of iterations and the final residue, can be obtain via the \fCp\&.option()\fP member function, see \fBsolver_option(4)\fP\&. Finally, the previous linear system is solved via the \fBsolver(4)\fP class: the \fCproblem\fP class is simply a convenient wrapper around the \fBsolver(4)\fP one\&.
.SH "EXAMPLE"
.PP
See \fBdirichlet\&.cc\fP
.SH "CUSTOMIZATION"
.PP
The \fBsolver(4)\fP could be customized via the constructor optional \fBsolver_option(4)\fP argument: 
.PP
.nf
    problem p (a, sopt);

.fi
.PP
 When using a direct \fBsolver(4)\fP, the determinant of the linear system matrix is also available as \fCp\&.det()\fP\&. When using an iterative \fBsolver(4)\fP, the preconditionner could be customized: 
.PP
.nf
    p\&.set_preconditionner (m);

.fi
.PP
 
.SH "TODO"
.PP
The \fCsolve\fP method could return a boolean when success\&.
.SH "IMPLEMENTATION"
.PP
This documentation has been generated from file main/lib/problem\&.h
.PP
The \fCproblem\fP class is simply an alias to the \fC\fBproblem_basic\fP\fP class
.PP
.PP
.nf
typedef problem_basic<Float> problem;
.fi
.PP
 
.PP
\fB\fP
.RS 4

.RE
.PP
The \fC\fBproblem_basic\fP\fP class provides a generic interface:
.PP
.PP
.nf
template <class T, class M = rheo_default_memory_model>
class problem_basic {
public:

// typedefs:
 
  typedef typename solver_basic<T,M>::size_type         size_type;
  typedef typename solver_basic<T,M>::determinant_type  determinant_type;

// allocators:

  problem_basic ();
  problem_basic (const form_basic<T,M>& a,
                 const solver_option& sopt = solver_option());

  void update_value (const form_basic<T,M>& a);

  void set_preconditioner (const solver_basic<T,M>&);

// accessor:

  void solve       (const field_basic<T,M>& lh, field_basic<T,M>& uh) const;
  void trans_solve (const field_basic<T,M>& lh, field_basic<T,M>& uh) const;

  determinant_type det() const;
  const solver_option& option() const;
  bool initialized() const;
.fi
.PP
 
.PP
.nf
};

.fi
.PP
 
.SH AUTHOR
Pierre  Saramito  <Pierre.Saramito@imag.fr>
.SH COPYRIGHT
Copyright   (C)  2000-2018  Pierre  Saramito  <Pierre.Saramito@imag.fr>
GPLv3+: GNU GPL version 3 or later  <http://gnu.org/licenses/gpl.html>.
This  is  free  software:  you  are free to change and redistribute it.
There is NO WARRANTY, to the extent permitted by law.