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LineEdge.cpp
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LineEdge.cpp
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#include <algorithm>
#include <cmath>
#include <iostream>
#include <vector>
using namespace std;
#include "LineEdge.h"
static double alphaExpStretch(double h) {
double alpha = 1.2;
for (int i = 0; i < 50; ++i) {
alpha = 0.5 * log(1. + 2. / h * alpha);
}
return alpha;
}
static double alphaSinStretch(double h) {
double alpha = 1.4;
for (int i = 0; i < 50; ++i) {
alpha = 0.5 * acos(h * sin(2. * alpha) / (2. * alpha));
}
return alpha;
}
static double alphaSin2Stretch(double h0, double h1, double &alpha,
double &beta) {
alpha = 1.4;
beta = 0.;
double tatb = (h0 - h1) / (h0 + h1);
for (int i = 0; i < 50; ++i) {
alpha = beta -
acos(h0 * (sin(alpha + beta) - sin(-alpha + beta)) / (2. * alpha));
beta = atan(tatb / tan(alpha));
}
return alpha;
}
double ExpStretch0(double s, double h0) {
double alpha = alphaExpStretch(h0);
return -1. + (exp(s * alpha) - exp(-alpha)) / (exp(alpha) - exp(-alpha)) * 2.;
}
double ExpStretch1(double s, double h1) {
double alpha = alphaExpStretch(h1);
return -1. +
(-exp(-s * alpha) + exp(alpha)) / (-exp(-alpha) + exp(alpha)) * 2.;
}
double QuadStretch0(double s, double h0) {
double alpha = 0.5 * (1. - h0);
return alpha * (s * s - 1.) + s;
}
double QuadStretch1(double s, double h1) {
double alpha = -0.5 * (1. - h1);
return alpha * (s * s - 1.) + s;
}
double SinStretch0(double s, double h0) {
double alpha = alphaSinStretch(h0);
double beta = -alpha;
return -1. + 2. * (sin(alpha * s + beta) - sin(-alpha + beta)) /
(sin(alpha + beta) - sin(-alpha + beta));
}
double SinStretch1(double s, double h1) {
double alpha = alphaSinStretch(h1);
double beta = alpha;
return -1. + 2. * (sin(alpha * s + beta) - sin(-alpha + beta)) /
(sin(alpha + beta) - sin(-alpha + beta));
}
double SinStretch2(double s, double h0, double h1) {
double alpha, beta;
alphaSin2Stretch(h0, h1, alpha, beta);
return -1. + 2. * (sin(alpha * s + beta) - sin(-alpha + beta)) /
(sin(alpha + beta) - sin(-alpha + beta));
}
double LineEdge::BuildDiscretes(double ds0, double ds1) {
double ds;
if (m_refineType == BOUNDARYLAYER0) {
ds = ds0;
m_discretes = std::vector<double>(m_N + 1, -1.);
for (int i = 1; i <= m_nBLayers0; ++i) {
if (ds > (1. - m_discretes[i - 1]) / (m_N - i + 1)) {
m_nBLayers0 = i - 1;
break;
} else {
m_discretes[i] = m_discretes[i - 1] + ds;
ds *= m_q0;
}
}
ds = (1. - m_discretes[m_nBLayers0]) / (m_N - m_nBLayers0);
for (int i = m_nBLayers0 + 1; i <= m_N; ++i) {
m_discretes[i] = m_discretes[i - 1] + ds;
}
m_discretes[m_N] = 1.;
} else if (m_refineType == BOUNDARYLAYER1) {
ds = ds1;
m_discretes = std::vector<double>(m_N + 1, 1.);
for (int i = 1; i <= m_nBLayers1; ++i) {
if (ds > (1. + m_discretes[m_N - i + 1]) / (m_N - i + 1)) {
m_nBLayers1 = i - 1;
break;
} else {
m_discretes[m_N - i] = m_discretes[m_N - i + 1] - ds;
ds *= m_q1;
}
}
ds = (1. + m_discretes[m_N - m_nBLayers1]) / (m_N - m_nBLayers1);
for (int i = m_nBLayers1 + 1; i <= m_N; ++i) {
m_discretes[m_N - i] = m_discretes[m_N - i + 1] - ds;
}
m_discretes[0] = -1.;
} else if (m_refineType == BOUNDARYLAYER2) {
m_discretes = std::vector<double>(m_N + 1, -1.);
m_discretes[m_N] = 1.;
ds = ds0;
for (int i = 1; i <= m_nBLayers0; ++i) {
if (ds > (1. - m_discretes[i - 1]) / (m_N - i + 1)) {
m_nBLayers0 = i - 1;
break;
} else {
m_discretes[i] = m_discretes[i - 1] + ds;
ds *= m_q0;
}
}
ds = ds1;
for (int i = 1; i <= m_nBLayers1; ++i) {
if (ds > (m_discretes[m_N - i + 1] - m_discretes[m_nBLayers0]) /
(m_N - i + 1)) {
m_nBLayers1 = i - 1;
break;
} else {
m_discretes[m_N - i] = m_discretes[m_N - i + 1] - ds;
ds *= m_q1;
}
}
ds = (m_discretes[m_N - m_nBLayers1] - m_discretes[m_nBLayers0]) /
(m_N - m_nBLayers0 - m_nBLayers1);
if (ds <= 0) {
std::cout << "error: unsupported BL refine type for edge number [r] "
<< m_N << std::endl;
}
for (int i = m_nBLayers0 + 1; i < m_N - m_nBLayers1; ++i) {
m_discretes[i] = m_discretes[i - 1] + ds;
}
} else if (m_refineType == BOUNDARYLAYER4) {
m_discretes = std::vector<double>(m_N + 1, -1.);
m_discretes[m_N] = 1.;
ds = ds1;
for (int i = 1; i <= m_nBLayers1; ++i) {
m_discretes[m_N - i] = m_discretes[m_N - i + 1] - ds;
ds *= m_q1;
if (ds > (m_discretes[m_N - i] + 1.) / (m_N - i)) {
m_nBLayers1 = i;
break;
}
}
ds = ds0;
for (int i = 1; i <= m_nBLayers0; ++i) {
m_discretes[i] = m_discretes[i - 1] + ds;
ds *= m_q0;
if (ds > (m_discretes[m_N - m_nBLayers1] - m_discretes[i]) / (m_N - i)) {
m_nBLayers0 = i;
break;
}
}
ds = (m_discretes[m_N - m_nBLayers1] - m_discretes[m_nBLayers0]) /
(m_N - m_nBLayers0 - m_nBLayers1);
if (ds <= 0) {
std::cout << "error: unsupported BL refine type for edge number [r] "
<< m_N << std::endl;
}
for (int i = m_nBLayers0 + 1; i < m_N - m_nBLayers1; ++i) {
m_discretes[i] = m_discretes[i - 1] + ds;
}
} else if (m_refineType == SMALLSTRETCH0) {
int Nu = 0;
m_discretes.clear();
double stmp = -1.;
m_discretes.push_back(stmp);
double dstmp = ds0;
while (true) {
Nu = (1. - stmp) / ds1 + 0.5;
double dux = (1. - stmp) / Nu;
if (dstmp < dux) {
stmp += dstmp;
m_discretes.push_back(stmp);
dstmp *= m_q0;
} else {
break;
}
}
double dux = (1. - stmp) / Nu;
double tmpratio = dux / ds1;
if (tmpratio < 1.) {
tmpratio = 1. / tmpratio;
}
std::cout << "Segment [" << m_p0[0] << ", " << m_p1[0] << "](" << m_q1
<< "), right end " << ds1 << "->" << dux << "[" << tmpratio << "]"
<< std::endl;
for (int i = Nu - 1; i >= 0; --i) {
stmp = 1. - dux * i;
m_discretes.push_back(stmp);
}
m_N = m_discretes.size() - 1;
} else if (m_refineType == SMALLSTRETCH1) {
int Nu = 0;
m_discretes.clear();
double stmp = 1.;
m_discretes.push_back(stmp);
double dstmp = ds1;
while (true) {
Nu = (1. + stmp) / ds0 + 0.5;
double dux = (1. + stmp) / Nu;
if (dstmp < dux) {
stmp -= dstmp;
m_discretes.push_back(stmp);
dstmp *= m_q1;
} else {
break;
}
}
double dux = (1. + stmp) / Nu;
double tmpratio = dux / ds0;
if (tmpratio < 1.) {
tmpratio = 1. / tmpratio;
}
std::cout << "Segment [" << m_p0[0] << ", " << m_p1[0] << "](" << m_q1
<< "), left end " << ds0 << "->" << dux << "[" << tmpratio << "]"
<< std::endl;
for (int i = Nu - 1; i >= 0; --i) {
stmp = -1. + dux * i;
m_discretes.push_back(stmp);
}
std::reverse(m_discretes.begin(), m_discretes.end());
m_N = m_discretes.size() - 1;
}
return 0.;
}
double LineEdge::DiscreteStretch(double s, double h0, double h1) {
if (m_discretes.size() < m_N + 1)
BuildDiscretes(h0, h1);
double x = (s + 1.) / 2. * m_N;
if (x < 0.)
x = 0.;
int ilower = floor(x);
if (ilower == m_N)
return 1.;
return (x - ilower) * (m_discretes[ilower + 1] - m_discretes[ilower]) +
m_discretes[ilower];
}
LineEdge::LineEdge(double *p0, double *p1, int N, int refineType, double h0,
double h1) {
m_p0 = p0;
m_p1 = p1;
m_N = N;
m_refineType = refineType;
m_h0 = h0 * N;
m_h1 = h1 * N;
}
// s = [-1., 1.]
std::vector<double> LineEdge::Evaluate(double s) {
double Len = sqrt((m_p0[0] - m_p1[0]) * (m_p0[0] - m_p1[0]) +
(m_p0[1] - m_p1[1]) * (m_p0[1] - m_p1[1]));
m_g0 = m_h0 / Len;
m_g1 = m_h1 / Len;
std::vector<double> res(2, 0.);
if (m_refineType == EXPREFINE0) {
s = ExpStretch0(s, m_g0);
}
if (m_refineType == EXPREFINE1) {
s = ExpStretch1(s, m_g1);
}
if (m_refineType == SINREFINE0) {
s = SinStretch0(s, m_g0);
}
if (m_refineType == SINREFINE1) {
s = SinStretch1(s, m_g1);
}
if (m_refineType == SINREFINE2) {
s = SinStretch2(s, m_g0, m_g1);
}
if (m_refineType == QUDREFINE0) {
s = QuadStretch0(s, m_g0);
}
if (m_refineType == QUDREFINE1) {
s = QuadStretch1(s, m_g1);
}
if (m_refineType == BOUNDARYLAYER0 || m_refineType == BOUNDARYLAYER1 ||
m_refineType == BOUNDARYLAYER2 || m_refineType == BOUNDARYLAYER4 ||
m_refineType == SMALLSTRETCH0 || m_refineType == SMALLSTRETCH1) {
s = DiscreteStretch(s, m_g0 * 2., m_g1 * 2.);
}
for (int i = 0; i < 2; ++i) {
res[i] = 0.5 * (1. - s) * m_p0[i] + 0.5 * (s + 1.) * m_p1[i];
}
return res;
}
LineEdge::LineEdge(double *p0, double *p1, int N, int refineType, double h0,
double q0, int NBlayers0, double h1, double q1,
int NBlayers1) {
m_p0 = p0;
m_p1 = p1;
m_N = N;
m_refineType = refineType;
if ((BOUNDARYLAYER0 == refineType && (q0 < 1. || N <= NBlayers0)) ||
(BOUNDARYLAYER1 == refineType && (q1 < 1. || N <= NBlayers1)) ||
((BOUNDARYLAYER2 == refineType || BOUNDARYLAYER4 == refineType) &&
(q0 < 1. || q1 < 1. || N <= NBlayers0 + NBlayers1))) {
std::cout << "error: unsupported BL refine type for edge number " << N
<< std::endl;
}
m_h0 = h0;
m_h1 = h1;
m_q0 = q0;
m_q1 = q1;
m_nBLayers0 = NBlayers0;
m_nBLayers1 = NBlayers1;
}
LineEdge::LineEdge(double *p0, double *p1, int refineType, double h0, double h1,
double q) {
m_p0 = p0;
m_p1 = p1;
m_refineType = refineType;
if (refineType == SMALLSTRETCH0 && h0 > h1 ||
refineType == SMALLSTRETCH1 && h0 < h1 || q < 1.) {
std::cout
<< "error: incorrect definition for SMALLSTRETCH0 or SMALLSTRETCH1, "
<< h0 << ", " << h1 << std::endl;
exit(-1);
}
m_h0 = h0;
m_h1 = h1;
m_q0 = q;
m_q1 = q;
Evaluate(0.);
}
// int main()
// {
// double pts[2][2];
// pts[0][0] = -5.;
// pts[0][1] = 0.;
// pts[1][0] = -1.;
// pts[1][1] = 0.;
// LineEdge Cedge2(pts[0], pts[1], SMALLSTRETCH1, 0.05, 0.01, 1.05);
// double ds = 2./Cedge2.m_N;
// for(int i=0; i<=Cedge2.m_N; ++i) {
// printf("%lf %lf\n", Cedge2.Evaluate(ds*i-1.)[0],
// Cedge2.Evaluate(ds*i-1.)[1]);
// }
// printf("\n");
// }
// int main()
// {
// double pts[2][2];
// pts[0][0] = -1.;
// pts[0][1] = 0.;
// pts[1][0] = 1.;
// pts[1][1] = 0.;
// int N=10;
// double ds = 2./N;
// LineEdge Cedge2(pts[0], pts[1], N , BOUNDARYLAYER2, 0.1, 2. , 4, 0.2, 1.,
// 2); LineEdge Cedge3(pts[1], pts[0], N , BOUNDARYLAYER4, 0.2, 1., 2,
// 0.1, 2. , 4); for(int i=0; i<=N; ++i) {
// printf("%lf ", Cedge2.Evaluate(ds*i-1.)[0]);
// }
// printf("\n");
// for(int i=N; i>=0; --i) {
// printf("%lf ", Cedge3.Evaluate(ds*i-1.)[0]);
// }
// printf("\n");
// }