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/*
* Copyright 2014-2015 Anton Khirnov <anton@khirnov.net>
*
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
/**
* @file
* definitions of the basis functions for the spectral method
*/
#include <math.h>
#include "internal.h"
static double sb_even_eval(double coord, int idx, double sf)
{
double val = atan2(sf, coord);
idx *= 2; // even only
return sin((idx + 1) * val);
}
static double sb_even_eval_diff1(double coord, int idx, double sf)
{
double val = atan2(sf, coord);
idx *= 2; // even only
return - sf * (idx + 1) * cos((idx + 1) * val) / (SQR(sf) + SQR(coord));
}
static double sb_even_eval_diff2(double coord, int idx, double sf)
{
double val = atan2(sf, coord);
idx *= 2; // even only
return sf * (idx + 1) * (2 * coord * cos((idx + 1) * val) - sf * (idx + 1) * sin((idx + 1) * val)) / SQR(SQR(sf) + SQR(coord));
}
static double sb_even_colloc_point(int order, int idx, double sf)
{
double t;
idx = order - idx - 1;
t = (idx + 2) * M_PI / (2 * order + 2);
return sf / tan(t);
}
/*
* The basis of even (n = 2 * idx) SB functions (Boyd 2000, Ch 17.9)
* SB(x, n) = sin((n + 1) arccot(|x| / L))
* They are symmetric wrt origin and decay as odd powers of x in infinity.
*/
const BasisSet bdi_sb_even_basis = {
.eval = sb_even_eval,
.eval_diff1 = sb_even_eval_diff1,
.eval_diff2 = sb_even_eval_diff2,
.colloc_point = sb_even_colloc_point,
};
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