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def-ImplicitE.cpp
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def-ImplicitE.cpp
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///////////////////////////////////////////////////////////
//
// This file contains the definitions for the
// classes required to calculate the effect of the implicit
// electric field and collisions for the first order harmonic
///////////////////////////////////////////////////////////
//
// class Implicit_Efield::
//
//
///////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////
// Standard Libraries
#include <iostream>
#include <vector>
#include <valarray>
#include <complex>
#include <limits>
#include <math.h>
#include <stdio.h>
#include <float.h>
// My Libraries
#include "matrices.h"
// Declerations
#include "decl-nmethods.h"
#include "decl-input.h"
#include "decl-state.h"
#include "decl-vlasovmax.h"
#include "decl-actions.h"
#include "decl-RK.h"
#include "decl-fokkerplanck.h"
#include "decl-implicitE.h"
//**************************************************************
//**************************************************************
//**************************************************************
//*******THE CLASS FOR THE CURRENT DEFINITION ******************
//**************************************************************
//**************************************************************
//**************************************************************
//--------------------------------------------------------------
Electric_Field_Methods::Current_xyz::Current_xyz(Stat& Yin)
//--------------------------------------------------------------
// Constructor
//--------------------------------------------------------------
: jayx(Yin.FLD(0)),
jayy(Yin.FLD(0)),
jayz(Yin.FLD(0)),
p3og(Inputdata::IN().inp().pr.dim(),
static_cast< complex<double> >(Inputdata::IN().inp().pr(0)),
static_cast< complex<double> >(Inputdata::IN().inp().pr(Inputdata::IN().inp().pr.dim()-1))),
Delta_p(static_cast< complex<double> >(Inputdata::IN().inp().pr.dx())),
small(static_cast< complex<double> >(Inputdata::IN().inp().pr(0)))
{
for (size_t i(0); i<p3og.dim(); ++i) { // calculate p^3/g
p3og(i) = (p3og(i)*p3og(i))*(p3og(i)/sqrt(1.0+p3og(i)*p3og(i)));
}
small *= small; small *= small; small *= Inputdata::IN().inp().pr(0);
small *= 0.2; small *= 1.0/(Inputdata::IN().inp().pr(1));
}
//--------------------------------------------------------------
//--------------------------------------------------------------
Field2D& Electric_Field_Methods::Current_xyz::J(int component) {
//--------------------------------------------------------------
// Return the current component 1 --> x, 2 --> y, 3 --> z
//--------------------------------------------------------------
switch (component) {
case 1: {
return Jx();
break;
}
case 2: {
return Jy();
break;
}
case 3: {
return Jz();
break;
}
default: {
cout << "There is no such component for the current! \n";
exit(1);
break;
}
}
return Jx();
}
//--------------------------------------------------------------
//--------------------------------------------------------------
Field2D& Electric_Field_Methods::Current_xyz::Jx() {
return jayx;
}
//--------------------------------------------------------------
//--------------------------------------------------------------
Field2D& Electric_Field_Methods::Current_xyz::Jy() {
return jayy;
}
//--------------------------------------------------------------
//--------------------------------------------------------------
Field2D& Electric_Field_Methods::Current_xyz::Jz() {
return jayz;
}
//--------------------------------------------------------------
//--------------------------------------------------------------
void Electric_Field_Methods::
Current_xyz::calculate_J(Stat& Yin) { //WHY- same as Vlasovmax: Current_Jxyz, but save Jxyz in JN.jay_xyz
//--------------------------------------------------------------
// Update the total current
//--------------------------------------------------------------
complex<double> c01(0.0,1.0);
SHarmonic f10(Yin.SH(1,0));
SHarmonic f11(Yin.SH(1,1));
f10 = f10.mpaxis(p3og.array());
f11 = f11.mpaxis(p3og.array());
// - - - - - - - - - - - - - - - - -
// Basic integration
for (size_t ix(0); ix < f10.numx(); ++ix){
for (size_t iy(0); iy < f10.numy(); ++iy){
jayx(ix,iy) = f10(0,ix,iy);
jayx(ix,iy) += f10(f10.nump()-1,ix,iy);
jayx(ix) *= 0.5;
for (size_t ip(1); ip < f10.nump()-1; ++ip) jayx(ix,iy)+= f10(ip,ix,iy);
}
}
jayx *= Delta_p;
// Add tiny contribution from 0-p0
for (size_t ix(0); ix < f10.numx(); ++ix){
for (size_t iy(0); iy < f10.numy(); ++iy){
jayx(ix,iy) += small*f10(1,ix,iy);
}
}
// Calculate the final current (minus is for electrons)
jayx *= (-4.0) * M_PI / 3.0;
// - - - - - - - - - - - - - - - - -
// Basic integration of the complex "current"
for (size_t ix(0); ix < f11.numx(); ++ix){
for (size_t iy(0); iy < f11.numy(); ++iy){
jayz(ix,iy) = f11(0,ix,iy);
jayz(ix,iy) += f11(f11.nump()-1,ix,iy);
jayz(ix) *= 0.5;
for (size_t ip(1); ip < f11.nump()-1; ++ip) jayz(ix,iy)+= f11(ip,ix,iy);
}
}
jayz *= Delta_p;
// Add tiny contribution from 0-p0
for (size_t ix(0); ix < f11.numx(); ++ix){
for (size_t iy(0); iy < f11.numy(); ++iy){
jayz(ix,iy) += small*f11(1,ix,iy);
}
}
// Calculate the final complex current
jayz *= (-8.0) * M_PI / 3.0;
// Calculate Jy
jayy = jayz; jayy = jayy.Re();
// Calculate Jz
jayz *= c01; jayz = jayz.Re();
}
//--------------------------------------------------------------
//--------------------------------------------------------------
void Electric_Field_Methods::
Current_xyz::calculate_J(int component, Stat& Yin) {
//--------------------------------------------------------------
// Update the current component 1 --> x, 2 --> y, 3 --> z
//--------------------------------------------------------------
switch (component) {
case 1: {
calculate_Jx(Yin);
break;
}
case 2: {
calculate_Jy(Yin);
break;
}
case 3: {
calculate_Jz(Yin);
break;
}
default: {
cout << "There is no such component for the current! \n";
exit(1);
break;
}
}
}
//--------------------------------------------------------------
//--------------------------------------------------------------
void Electric_Field_Methods::
Current_xyz::calculate_Jx(Stat& Yin) {
//--------------------------------------------------------------
// Update the current in x-direction
//--------------------------------------------------------------
SHarmonic f10(Yin.SH(1,0));
f10 = f10.mpaxis(p3og.array());
// Basic integration
for (size_t ix(0); ix < f10.numx(); ++ix){
for (size_t iy(0); iy < f10.numy(); ++iy){
jayx(ix,iy) = f10(0,ix,iy);
jayx(ix,iy) += f10(f10.nump()-1,ix,iy);
jayx(ix) *= 0.5;
for (size_t ip(1); ip < f10.nump()-1; ++ip) jayx(ix,iy)+= f10(ip,ix,iy);
}
}
jayx *= Delta_p;
// Add tiny contribution from 0-p0
for (size_t ix(0); ix < f10.numx(); ++ix){
for (size_t iy(0); iy < f10.numy(); ++iy){
jayx(ix,iy) += small*f10(1,ix,iy);
}
}
// Calculate final current (minus is for electrons)
jayx *= (-4.0) * M_PI / 3.0;
}
//--------------------------------------------------------------
//--------------------------------------------------------------
void Electric_Field_Methods::
Current_xyz::calculate_Jy(Stat& Yin) {
//--------------------------------------------------------------
// Update the current in y-direction
//--------------------------------------------------------------
SHarmonic f11(Yin.SH(1,1));
f11 = f11.mpaxis(p3og.array());
// - - - - - - - - - - - - - - - - -
// Basic integration of the complex "current"
for (size_t ix(0); ix < f11.numx(); ++ix){
for (size_t iy(0); iy < f11.numy(); ++iy){
jayy(ix,iy) = f11(0,ix,iy);
jayy(ix,iy) += f11(f11.nump()-1,ix,iy);
jayy(ix) *= 0.5;
for (size_t ip(1); ip < f11.nump()-1; ++ip) jayy(ix,iy)+= f11(ip,ix,iy);
}
}
jayy *= Delta_p;
// Add tiny contribution from 0-p0
for (size_t ix(0); ix < f11.numx(); ++ix){
for (size_t iy(0); iy < f11.numy(); ++iy){
jayy(ix,iy) += small*f11(1,ix,iy);
}
}
// Calculate the final complex current
jayy *= (-8.0) * M_PI / 3.0;
// Calculate Jy
jayy = jayy.Re();
}
//--------------------------------------------------------------
//--------------------------------------------------------------
void Electric_Field_Methods::
Current_xyz::calculate_Jz(Stat& Yin) {
//--------------------------------------------------------------
// Update the total current
//--------------------------------------------------------------
complex<double> c01(0.0,1.0);
SHarmonic f11(Yin.SH(1,1));
f11 = f11.mpaxis(p3og.array());
// - - - - - - - - - - - - - - - - -
// Basic integration of the complex "current"
for (size_t ix(0); ix < f11.numx(); ++ix){
for (size_t iy(0); iy < f11.numy(); ++iy){
jayz(ix,iy) = f11(0,ix,iy);
jayz(ix,iy) += f11(f11.nump()-1,ix,iy);
jayz(ix) *= 0.5;
for (size_t ip(1); ip < f11.nump()-1; ++ip) jayz(ix,iy)+= f11(ip,ix,iy);
}
}
jayz *= Delta_p;
// Add tiny contribution from 0-p0
for (size_t ix(0); ix < f11.numx(); ++ix){
for (size_t iy(0); iy < f11.numy(); ++iy){
jayz(ix,iy) += small*f11(1,ix,iy);
}
}
// Calculate the final complex current
jayz *= (-8.0) * M_PI / 3.0;
// Calculate Jz
jayz *= c01; jayz = jayz.Re();
}
//--------------------------------------------------------------
//**************************************************************
//**************************************************************
//--------------------------------------------------------------
Electric_Field_Methods::Efield_xyz::Efield_xyz(Stat& Yin)
//--------------------------------------------------------------
// Constructor
//--------------------------------------------------------------
: efieldx(Yin.FLD(0)),
efieldy(Yin.FLD(1)),
efieldz(Yin.FLD(2)) {
}
//--------------------------------------------------------------
//--------------------------------------------------------------
Field2D& Electric_Field_Methods::Efield_xyz::E(int component) {
//--------------------------------------------------------------
// Return the current component 1 --> x, 2 --> y, 3 --> z
//--------------------------------------------------------------
switch (component) {
case 1: {
return Ex();
break;
}
case 2: {
return Ey();
break;
}
case 3: {
return Ez();
break;
}
default: {
cout << "There is no such component for the current! \n";
exit(1);
break;
}
}
return Ex();
}
//--------------------------------------------------------------
//--------------------------------------------------------------
Field2D& Electric_Field_Methods::Efield_xyz::Ex() {
return efieldx;
}
//--------------------------------------------------------------
//--------------------------------------------------------------
Field2D& Electric_Field_Methods::Efield_xyz::Ey() {
return efieldy;
}
//--------------------------------------------------------------
//--------------------------------------------------------------
Field2D& Electric_Field_Methods::Efield_xyz::Ez() {
return efieldz;
}
//--------------------------------------------------------------
//**************************************************************
//**************************************************************
//--------------------------------------------------------------
// Definition of the pure virtual destructor for the abstract
// class Explicit_Method
//--------------------------------------------------------------
Electric_Field_Methods::Efield_Method::
~Efield_Method(){}
//**************************************************************
//**************************************************************
//--------------------------------------------------------------
Electric_Field_Methods::Explicit_E_Field::
Explicit_E_Field(Stat& Yin, int tout_start)
: t(static_cast<double>(tout_start) *
Inputdata::IN().cont().dt_out), // Initialize time
Y(Yin) {
}
//--------------------------------------------------------------
//--------------------------------------------------------------
void Electric_Field_Methods::Explicit_E_Field::
advance(Explicit_Method* rk, Euler_Backward* eb){ }
//--------------------------------------------------------------
//--------------------------------------------------------------
bool Electric_Field_Methods::Explicit_E_Field::
implicitE() const {
return false;
}
//--------------------------------------------------------------
//**************************************************************
//**************************************************************
//**************************************************************
// Definition for the implicit electric field
//**************************************************************
//**************************************************************
//**************************************************************
//--------------------------------------------------------------
Electric_Field_Methods::Implicit_E_Field::
Implicit_E_Field(Stat& Yin, int tout_start)
//--------------------------------------------------------------
// Constructor for the implicit electric field
//--------------------------------------------------------------
: t(static_cast<double>(tout_start) *
Inputdata::IN().cont().dt_out), // Initialize time
Y(Yin),
JN(Yin), J0(Yin), // New current, Current from E = 0
J_Ex(Yin), J_Ey(Yin), J_Ez(Yin), // Current due to the effect of Ex, Ey, Ez
EN(Yin), E0(Yin), DE(Yin), // New E, old E, perturbation E
f00(Y.SH(0,0)),
f10(f00), f11(f00), //WHY? in advance(), f10,..., f22 are redifined again
f20(f00), f21(f00), f22(f00),
if_implicitES(Inputdata::IN().list().if_implicitES),
if_implicit1D(Inputdata::IN().list().if_implicit1D),
l0(Inputdata::IN().inp().l0),
m0(Inputdata::IN().inp().m0),
idx(static_cast< complex<double> >(Inputdata::IN().inp().x.dx())),
idy(static_cast< complex<double> >(Inputdata::IN().inp().y.dx())) {
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
idx = -1.0/(2.0*idx);
idy = -1.0/(2.0*idy);
using Inputdata::IN;
Nbc = IN().list().RKLevel;
szx = IN().inp().x.dim();
szy = IN().inp().y.dim();
}
//--------------------------------------------------------------
//--------------------------------------------------------------
void Electric_Field_Methods::Implicit_E_Field::
advance(Explicit_Method* rk, Euler_Backward* eb){
//--------------------------------------------------------------
// Calculate the implicit electric field
//--------------------------------------------------------------
int zeros_in_det(1); // This counts the number of zeros in the determinant
int execution_attempt(0); // This counts the number of attempts to find invert the E-field
f00 = Y.SH(0,0);
f10 = Y.SH(1,0); f11 = Y.SH(1,1);
f20 = Y.SH(2,0); f21 = Y.SH(2,1); f22 = Y.SH(2,2);
FindDE(); // Reset DE //WHY- actually DE !=0, ~epsilon
// - - - - - - - - - - - - - - - - - - - - - -
while ( (zeros_in_det > 0) && ( execution_attempt < 4) ) { // Execute this loop at most twice //WHY? twice? but <4
zeros_in_det = 0; // Count the zeros of the determinant
++execution_attempt; // Count the execusion attempts
// - - - - - - - - - - - - - - - - - - - - - -
// - - - - - - - - - - - - - - - - - - - - - -
// Effect of E = 0 on f00, f10, f11
(*eb).advance_1((*rk).time()); // Collisions for f10, f11
J0.calculate_J(Y); //WHY? E=0? it seems E=En
Y.SH(0,0) = f00; //WHY- after getting J0, recover Y..
Y.SH(1,0) = f10; Y.SH(1,1) = f11;
// - - - - - - - - - - - - - - - - - - - - - -
Y.EMF().Ex() = DE.Ex(); // Ex = DEx
(*rk).advance_IEx(); // Effect of DEx on Y00, Y10, Y11, Y20, Y21, Y22
(*eb).advance_1((*rk).time()); // Collisions for Y10, Y11
J_Ex.calculate_J(Y); // Evaluate J(DEx)
Y.SH(0,0) = f00;
Y.SH(1,0) = f10; Y.SH(1,1) = f11;
Y.SH(2,0) = f20; Y.SH(2,1) = f21; Y.SH(2,2) = f22;
// - - - - - - - - - - - - - - - - - - - - - -
if ( !(if_implicit1D) ) { //WHY- implicit1D == false, always do this
Y.EMF().Ey() = DE.Ey(); // Ey = DEy
(*rk).advance_IEy(); // Effect of DEy on Y00, Y10, Y11, Y20, Y21, Y22
(*eb).advance_1((*rk).time()); // Collisions for Y10, Y11
J_Ey.calculate_J(Y); // Evaluate J(DEy)
Y.SH(0,0) = f00;
Y.SH(1,0) = f10; Y.SH(1,1) = f11;
Y.SH(2,0) = f20; Y.SH(2,1) = f21; Y.SH(2,2) = f22;
// - - - - - - - - - - - - - - - - - - - - - -
Y.EMF().Ez() = DE.Ez(); // Ez = DEz
(*rk).advance_IEz(); // Effect of DEz on Y00, Y10, Y11, Y20, Y21, Y22
(*eb).advance_1((*rk).time()); // Collisions for Y10, Y11
J_Ez.calculate_J(Y); // Evaluate J(DEz)
Y.SH(0,0) = f00;
Y.SH(1,0) = f10; Y.SH(1,1) = f11;
Y.SH(2,0) = f20; Y.SH(2,1) = f21; Y.SH(2,2) = f22;
// - - - - - - - - - - - - - - - - - - - - - -
if ( !(if_implicitES) ) {
Ampere(); // Calculate JN
}
}
// - - - - - - - - - - - - - - - - - - - - - -
// calculate new EN
Matrix2D< complex<double> > sgm(3,3);
valarray< complex<double> > clm(3);
if ( !(if_implicit1D) ) {
for (size_t iy(0); iy < szy; ++iy){
for (size_t ix(0); ix < szx; ++ix){
sgm(0,0) = ( J_Ex.Jx()(ix,iy) - J0.Jx()(ix,iy) ) / DE.Ex()(ix,iy); // sxx = dJ(E_x)_x/DE_x
sgm(0,1) = ( J_Ey.Jx()(ix,iy) - J0.Jx()(ix,iy) ) / DE.Ey()(ix,iy); // sxy = dJ(E_y)_x/DE_y
sgm(0,2) = ( J_Ez.Jx()(ix,iy) - J0.Jx()(ix,iy) ) / DE.Ez()(ix,iy); // sxz = dJ(E_z)_x/DE_z
sgm(1,0) = ( J_Ex.Jy()(ix,iy) - J0.Jy()(ix,iy) ) / DE.Ex()(ix,iy); // syx = dJ(E_x)_y/DE_x
sgm(1,1) = ( J_Ey.Jy()(ix,iy) - J0.Jy()(ix,iy) ) / DE.Ey()(ix,iy); // syy = dJ(E_y)_y/DE_y
sgm(1,2) = ( J_Ez.Jy()(ix,iy) - J0.Jy()(ix,iy) ) / DE.Ez()(ix,iy); // syz = dJ(E_z)_y/DE_z
sgm(2,0) = ( J_Ex.Jz()(ix,iy) - J0.Jz()(ix,iy) ) / DE.Ex()(ix,iy); // szx = dJ(E_x)_z/DE_x
sgm(2,1) = ( J_Ey.Jz()(ix,iy) - J0.Jz()(ix,iy) ) / DE.Ey()(ix,iy); // szy = dJ(E_y)_z/DE_y
sgm(2,2) = ( J_Ez.Jz()(ix,iy) - J0.Jz()(ix,iy) ) / DE.Ez()(ix,iy); // szz = dJ(E_z)_z/DE_z
clm[0] = JN.Jx()(ix,iy) - J0.Jx()(ix,iy);
clm[1] = JN.Jy()(ix,iy) - J0.Jy()(ix,iy);
clm[2] = JN.Jz()(ix,iy) - J0.Jz()(ix,iy);
// Solve the 3 by 3 system of equations
complex<double> D_sgm( Det33(sgm) ); // The Determinant of the conductivity tensor
if ( abs( D_sgm.real() ) > 6.0*DBL_MIN ) {
EN.Ex()(ix,iy) = Detx33(clm, sgm) / D_sgm;
EN.Ey()(ix,iy) = Dety33(clm, sgm) / D_sgm;
EN.Ez()(ix,iy) = Detz33(clm, sgm) / D_sgm;
}
else {
++zeros_in_det; // Try again with a new perturbation as below
DE.Ex()(ix,iy) *= 2; // DEx is 2 times larger than before
DE.Ey()(ix,iy) *= 1.3; // DEy is 1.3 times larger than before
EN.Ex()(ix,iy) = 0.0;
EN.Ey()(ix,iy) = 0.0;
EN.Ez()(ix,iy) = 0.0;
}
}
}
}
else {
for (size_t iy(0); iy < szy; ++iy){
for (size_t ix(0); ix < szx; ++ix){
// Solution for alculation JN = 0
EN.Ex()(ix,iy) = DE.Ex()(ix,iy) * J0.Jx()(ix,iy)
/( J0.Jx()(ix,iy) - J_Ex.Jx()(ix,iy) );
EN.Ey()(ix,iy) = 0.0;// DE.Ey()(ix,iy) * J0.Jy()(ix,iy)
EN.Ez()(ix,iy) = 0.0;// DE.Ey()(ix,iy) * J0.Jy()(ix,iy)
// EN.Ey()(ix,iy) = DE.Ey()(ix,iy) * J0.Jy()(ix,iy)
// /( J0.Jy()(ix,iy) - J_Ey.Jy()(ix,iy) );
}
}
}
// - - - - - - - - - - - - - - - - - - - - - -
} // End the while statement
// - - - - - - - - - - - - - - - - - - - - - -
// - - - - - - - - - - - - - - - - - - - - - -
Y.EMF().Ex() = EN.Ex();
Y.EMF().Ey() = EN.Ey();
Y.EMF().Ez() = EN.Ez();
if ( zeros_in_det > 0) {
cout << "WARNING, Det = 0 in "<<zeros_in_det <<"locations \n";
if ( zeros_in_det > 8) { exit(1);}
}
}
//--------------------------------------------------------------
//--------------------------------------------------------------
bool Electric_Field_Methods::Implicit_E_Field::
implicitE() const {
return true;
}
//--------------------------------------------------------------
//--------------------------------------------------------------
void Electric_Field_Methods::Implicit_E_Field::FindDE(){
//--------------------------------------------------------------
// Reset DE
//--------------------------------------------------------------
double Eps(16.0*numeric_limits<double>::epsilon()); //WHY- very small number
double LargeEps(sqrt(Eps));
DE.Ex() = Y.EMF().Ex();
DE.Ey() = Y.EMF().Ey();
DE.Ez() = Y.EMF().Ez();
// Calculate DEx = LargeEps*(|E|)+Eps
for (size_t iy(0); iy < szy; ++iy){
for (size_t ix(0); ix < szx; ++ix){
DE.Ex()(ix,iy) *= DE.Ex()(ix,iy);
DE.Ey()(ix,iy) *= DE.Ey()(ix,iy);
DE.Ez()(ix,iy) *= DE.Ez()(ix,iy);
DE.Ex()(ix,iy) += DE.Ey()(ix,iy);
DE.Ex()(ix,iy) += DE.Ez()(ix,iy);
DE.Ex()(ix,iy) = sqrt(DE.Ex()(ix,iy));
DE.Ex()(ix,iy) *= LargeEps;
DE.Ex()(ix,iy) += Eps;
}
}
DE.Ey() = DE.Ex();
DE.Ez() = DE.Ex();
}
//--------------------------------------------------------------
//--------------------------------------------------------------
void Electric_Field_Methods::Implicit_E_Field::Ampere(){
//--------------------------------------------------------------
// Use Ampere's law to calculate JN
//--------------------------------------------------------------
Field2D tmpJi(Y.EMF().Bz());
// Jx = dBz/dy
// tmpJi = Yin.EMF().Bz(); (same as assignment above)
tmpJi *= idy;
JN.Jx() = tmpJi.Dy();
// Jy = -dBz/dx
tmpJi = Y.EMF().Bz();
tmpJi *= (-1.0) * idx;
JN.Jy() = tmpJi.Dx();
// Jz = -dBx/dy
tmpJi = Y.EMF().Bx();
tmpJi *= (-1.0) * idy;
JN.Jz() = tmpJi.Dy();
// Jz += dBy/dx
tmpJi = Y.EMF().By();
tmpJi *= idx;
JN.Jz() += tmpJi.Dx();
}
//--------------------------------------------------------------
//**************************************************************