.TH "interpolate" 3rheolef "Mon Sep 19 2022" "Version 7.2" "rheolef" \" -*- nroff -*-
.ad l
.nh
.SH NAME
interpolate \- function or expression interpolation (rheolef-7\&.2)
.SH "DESCRIPTION"
.PP
The \fCinterpolation\fP function implements the usual Lagrange interpolation of a function or a class-function on a finite element \fBspace(2)\fP\&.
.SH "SYNOPSIS"
.PP
.PP
.nf
    template <class Expression>
    field interpolate (const space& Xh, const Expression& expr);
.fi
.PP
 Example The following code compute the Lagrange interpolation \fCpi_h_u\fP the function \fCu(x)\fP: 
.PP
.nf
   Float u(const point& x) { return exp(x[0]*x[1]); }
   \&.\&.\&.
   geo omega('square');
   space Xh (omega, 'P1');
   field pi_h_u = interpolate (Xh, u);

.fi
.PP
 
.SH "EXPRESSIONS"
.PP
It is possible to interpolate an expression involving a combination of functions, class-functions and fields: 
.PP
.nf
    field vh = interpolate (Xh, sqrt(uh) + 2*max(0\&.,uh));

.fi
.PP
 
.SH "REINTERPOLATION"
.PP
The reinterpolation of a field on another mesh or on another finite element space is also possible: 
.PP
.nf
    geo omega2 ('square2');
    space X2h (omega2, 'P1');
    field uh2 = interpolate (X2h, pi_h_u);

.fi
.PP
 Such a reinterpolation is very frequent in mesh adaptive loops\&.
.SH "IMPLEMENTATION"
.PP
This documentation has been generated from file main/lib/interpolate\&.h
.PP
The implementation of expressions bases on the \fCexpression template\fP and \fCSFINAE\fP C++ idioms\&. 
.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.