YA4MOIT3DE4SVND7DRAUDIOKPNXHNB4IYYZYBEV757BBXEGY4BUAC zero charge: aphi = aA k omega / k^2
ht omega = -I (ax/dx (-1 + E^(I dx kx)) + ay/dy (-1 + E^(I dy ky)) + az/dz (-1 + E^(I dz kz)))ht omega = -i (ax/dx (exp i kx dx/2) (2 i sin (kx dx/2)) + ay/dy (exp i ky dy/2) (2 i sin (ky dy/2)) + az/dz (exp i kz dz/2) (2 i sin (kz dz/2)))ht omega = ax kx (exp i kx dx/2) sinc(kx dx/2) + ay ky (exp i ky dy/2) sinc(ky dy/2)) + az kz (exp i kz dz/2) sinc(kz dz/2)4. Discrete ansatz:- Choose E and B field- Choose phi and A analytically- Calculate E and B discretely to ensure constraintsEx = cos (omega t - kz z)Ey = 0Ez = 0Byz = 0Bzx = cos (omega t - kz z)Bxy = 0phi = 0E = curl CCx = 0Cy = 1/kz sin (omega t - kz z)Cz = 0Ax = -1/kz sin (omega t - kz z)Ay = 0Az = 0
CCTK_REAL curlax TYPE=gf TAGS='index={0 1 1} checkpoint="no"' "Magnetic potential constraint"CCTK_REAL curlay TYPE=gf TAGS='index={1 0 1} checkpoint="no"' "Magnetic potential constraint"CCTK_REAL curlaz TYPE=gf TAGS='index={1 1 0} checkpoint="no"' "Magnetic potential constraint"
CCTK_REAL curlayz TYPE=gf TAGS='index={0 1 1} checkpoint="no"' "Magnetic potential constraint"CCTK_REAL curlazx TYPE=gf TAGS='index={1 0 1} checkpoint="no"' "Magnetic potential constraint"CCTK_REAL curlaxy TYPE=gf TAGS='index={1 1 0} checkpoint="no"' "Magnetic potential constraint"
# Cell-centred variablesCCTK_REAL avgphi TYPE=gf TAGS='checkpoint="no"' "Averaged electric potential"CCTK_REAL avga TYPE=gf TAGS='checkpoint="no"' { avgax avgay avgaz } "Averaged magnetic potential"CCTK_REAL avge TYPE=gf TAGS='checkpoint="no"' { avgex avgey avgez } "Averaged electric field"CCTK_REAL avgb TYPE=gf TAGS='checkpoint="no"' { avgbyz avgbzx avgbxy } "Averaged magnetic field"CCTK_REAL avgcurla TYPE=gf TAGS='checkpoint="no"' { avgcurlyz avgcurlzx avgcurlxy } "Averaged magnetic potential constraint"CCTK_REAL avgdive TYPE=gf TAGS='checkpoint="no"' "Averaged electric constraint"CCTK_REAL avgdivb TYPE=gf TAGS='checkpoint="no"' "Averaged magnetic constraint"# CCTK_REAL phi1 TYPE=gf TAGS='index={0 0 0}' "Electric potential"# CCTK_REAL dive1 TYPE=gf TAGS='index={0 0 0}' "Electric constraint"
# SCHEDULE Maxwell_EstimateError AT postinitial# {# LANG: C# READS: phi(everywhere)# READS: ax(everywhere) ay(everywhere) az(everywhere)# READS: ex(everywhere) ey(everywhere) ez(everywhere)# READS: byz(everywhere) bzx(everywhere) bxy(everywhere)# WRITES: CarpetX::regrid_error(interior)# } "Estimate local error for regridding initial conditions"# SCHEDULE Maxwell_Constraints AT postinitial# {# LANG: C# READS: ax(interior) ay(interior) az(interior)# READS: ex(everywhere) ey(everywhere) ez(everywhere)# READS: byz(interior) bzx(interior) bxy(interior)# WRITES: curlayz(interior) curlazx(interior) curlaxy(interior)# WRITES: dive(interior)# WRITES: divb(interior)# SYNC: curlayz curlazx curlaxy# SYNC: dive# SYNC: divb# } "Calculate constraints"## SCHEDULE Maxwell_Solve AT postinitial AFTER Maxwell_Constraints# {# LANG: C# OPTIONS: global# READS: dive(interior)# WRITES: phi1(interior)# # WRITES: dive1(interior)# } "Solve div E constraint"## SCHEDULE Maxwell_UpdatePhi AT postinitial AFTER Maxwell_Solve# {# LANG: C# READS: phi(interior)# READS: phi1(interior)# WRITES: phi(interior)# INVALIDATES: phi1(interior)# # INVALIDATES: dive1(interior)# INVALIDATES: curlayz(everywhere) curlazx(everywhere) curlaxy(everywhere)# INVALIDATES: dive(everywhere)# INVALIDATES: divb(everywhere)# SYNC: phi# } "Update electric potential"# SCHEDULE Maxwell_Average AT postinitial AFTER Maxwell_Constraints# {# LANG: C# READS: phi(interior)# READS: ax(interior) ay(interior) az(interior)# READS: ex(interior) ey(interior) ez(interior)# READS: byz(interior) bzx(interior) bxy(interior)# READS: curlayz(interior) curlazx(interior) curlaxy(interior)# READS: dive(interior)# READS: divb(interior)# WRITES: avgphi(interior)# WRITES: avga(interior)# WRITES: avge(interior)# WRITES: avgb(interior)# WRITES: avgcurla(interior)# WRITES: avgdive(interior)# WRITES: avgdivb(interior)# SYNC: avgphi# SYNC: avga# SYNC: avge# SYNC: avgb# SYNC: avgcurla# SYNC: avgdive# SYNC: avgdivb# } "Average to cell-centred values"
SCHEDULE Maxwell_EstimateError AT postinitial AFTER (Maxwell_Average, Maxwell_Solve){LANG: C# READS: avgphi(everywhere)# READS: avga(everywhere)# READS: avge(everywhere)# READS: avgb(everywhere)WRITES: CarpetX::regrid_error(interior)} "Estimate local error for regridding during evolution"
# SCHEDULE Maxwell_EstimateError AT poststep# {# LANG: C# READS: phi(everywhere)# READS: ax(everywhere) ay(everywhere) az(everywhere)# READS: ex(everywhere) ey(everywhere) ez(everywhere)# READS: byz(everywhere) bzx(everywhere) bxy(everywhere)# WRITES: CarpetX::regrid_error(interior)# } "Estimate local error for regridding during evolution"SCHEDULE Maxwell_Average AT poststep AFTER Maxwell_Constraints{LANG: CREADS: phi(interior)READS: ax(interior) ay(interior) az(interior)READS: ex(interior) ey(interior) ez(interior)READS: byz(interior) bzx(interior) bxy(interior)READS: curlayz(interior) curlazx(interior) curlaxy(interior)READS: dive(interior)READS: divb(interior)WRITES: avgphi(interior)WRITES: avga(interior)WRITES: avge(interior)WRITES: avgb(interior)WRITES: avgcurla(interior)WRITES: avgdive(interior)WRITES: avgdivb(interior)SYNC: avgphiSYNC: avgaSYNC: avgeSYNC: avgbSYNC: avgcurlaSYNC: avgdiveSYNC: avgdivb} "Average to cell-centred values"SCHEDULE Maxwell_EstimateError AT poststep AFTER Maxwell_Average{LANG: C# READS: avgphi(everywhere)# READS: avga(everywhere)# READS: avge(everywhere)# READS: avgb(everywhere)WRITES: CarpetX::regrid_error(interior)} "Estimate local error for regridding during evolution"
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#include <loop.hxx>#include <cctk.h>#include <cctk_Arguments_Checked.h>#include <cctk_Parameters.h>namespace Maxwell {namespace {template <typename T, int CI, int CJ, int CK>T average(const Loop::GF3D<const T, CI, CJ, CK> &var,const Loop::PointDesc &p) {const auto DI = Loop::vect<int, Loop::dim>::unit(0);const auto DJ = Loop::vect<int, Loop::dim>::unit(1);const auto DK = Loop::vect<int, Loop::dim>::unit(2);T res = 0;for (int k = 0; k < 2 - CK; ++k)for (int j = 0; j < 2 - CJ; ++j)for (int i = 0; i < 2 - CI; ++i)res += var(p.I + i * DI + j * DJ + k * DK);return res / ((2 - CI) * (2 - CJ) * (2 - CK));}} // namespaceextern "C" void Maxwell_Average(CCTK_ARGUMENTS) {DECLARE_CCTK_ARGUMENTS_Maxwell_Average;DECLARE_CCTK_PARAMETERS;const Loop::GF3D<const CCTK_REAL, 0, 0, 0> phi_(cctkGH, phi);const Loop::GF3D<const CCTK_REAL, 1, 0, 0> ax_(cctkGH, ax);const Loop::GF3D<const CCTK_REAL, 0, 1, 0> ay_(cctkGH, ay);const Loop::GF3D<const CCTK_REAL, 0, 0, 1> az_(cctkGH, az);const Loop::GF3D<const CCTK_REAL, 1, 0, 0> ex_(cctkGH, ex);const Loop::GF3D<const CCTK_REAL, 0, 1, 0> ey_(cctkGH, ey);const Loop::GF3D<const CCTK_REAL, 0, 0, 1> ez_(cctkGH, ez);const Loop::GF3D<const CCTK_REAL, 0, 1, 1> byz_(cctkGH, byz);const Loop::GF3D<const CCTK_REAL, 1, 0, 1> bzx_(cctkGH, bzx);const Loop::GF3D<const CCTK_REAL, 1, 1, 0> bxy_(cctkGH, bxy);const Loop::GF3D<const CCTK_REAL, 0, 1, 1> curlayz_(cctkGH, curlayz);const Loop::GF3D<const CCTK_REAL, 1, 0, 1> curlazx_(cctkGH, curlazx);const Loop::GF3D<const CCTK_REAL, 1, 1, 0> curlaxy_(cctkGH, curlaxy);const Loop::GF3D<const CCTK_REAL, 0, 0, 0> dive_(cctkGH, dive);const Loop::GF3D<const CCTK_REAL, 1, 1, 1> divb_(cctkGH, divb);const Loop::GF3D<CCTK_REAL, 1, 1, 1> avgphi_(cctkGH, avgphi);const Loop::GF3D<CCTK_REAL, 1, 1, 1> avgax_(cctkGH, avgax);const Loop::GF3D<CCTK_REAL, 1, 1, 1> avgay_(cctkGH, avgay);const Loop::GF3D<CCTK_REAL, 1, 1, 1> avgaz_(cctkGH, avgaz);const Loop::GF3D<CCTK_REAL, 1, 1, 1> avgex_(cctkGH, avgex);const Loop::GF3D<CCTK_REAL, 1, 1, 1> avgey_(cctkGH, avgey);const Loop::GF3D<CCTK_REAL, 1, 1, 1> avgez_(cctkGH, avgez);const Loop::GF3D<CCTK_REAL, 1, 1, 1> avgbyz_(cctkGH, avgbyz);const Loop::GF3D<CCTK_REAL, 1, 1, 1> avgbzx_(cctkGH, avgbzx);const Loop::GF3D<CCTK_REAL, 1, 1, 1> avgbxy_(cctkGH, avgbxy);const Loop::GF3D<CCTK_REAL, 1, 1, 1> avgcurlayz_(cctkGH, avgcurlyz);const Loop::GF3D<CCTK_REAL, 1, 1, 1> avgcurlazx_(cctkGH, avgcurlzx);const Loop::GF3D<CCTK_REAL, 1, 1, 1> avgcurlaxy_(cctkGH, avgcurlxy);const Loop::GF3D<CCTK_REAL, 1, 1, 1> avgdive_(cctkGH, avgdive);const Loop::GF3D<CCTK_REAL, 1, 1, 1> avgdivb_(cctkGH, avgdivb);Loop::loop_int<1, 1, 1>(cctkGH, [&](const Loop::PointDesc &p) {avgphi_(p.I) = average(phi_, p);});Loop::loop_int<1, 1, 1>(cctkGH, [&](const Loop::PointDesc &p) { avgax_(p.I) = average(ax_, p); });Loop::loop_int<1, 1, 1>(cctkGH, [&](const Loop::PointDesc &p) { avgay_(p.I) = average(ay_, p); });Loop::loop_int<1, 1, 1>(cctkGH, [&](const Loop::PointDesc &p) { avgaz_(p.I) = average(az_, p); });Loop::loop_int<1, 1, 1>(cctkGH, [&](const Loop::PointDesc &p) { avgex_(p.I) = average(ex_, p); });Loop::loop_int<1, 1, 1>(cctkGH, [&](const Loop::PointDesc &p) { avgey_(p.I) = average(ey_, p); });Loop::loop_int<1, 1, 1>(cctkGH, [&](const Loop::PointDesc &p) { avgez_(p.I) = average(ez_, p); });Loop::loop_int<1, 1, 1>(cctkGH, [&](const Loop::PointDesc &p) {avgbyz_(p.I) = average(byz_, p);});Loop::loop_int<1, 1, 1>(cctkGH, [&](const Loop::PointDesc &p) {avgbzx_(p.I) = average(bzx_, p);});Loop::loop_int<1, 1, 1>(cctkGH, [&](const Loop::PointDesc &p) {avgbxy_(p.I) = average(bxy_, p);});Loop::loop_int<1, 1, 1>(cctkGH, [&](const Loop::PointDesc &p) {avgcurlayz_(p.I) = average(curlayz_, p);});Loop::loop_int<1, 1, 1>(cctkGH, [&](const Loop::PointDesc &p) {avgcurlazx_(p.I) = average(curlazx_, p);});Loop::loop_int<1, 1, 1>(cctkGH, [&](const Loop::PointDesc &p) {avgcurlaxy_(p.I) = average(curlaxy_, p);});Loop::loop_int<1, 1, 1>(cctkGH, [&](const Loop::PointDesc &p) {avgdive_(p.I) = average(dive_, p);});Loop::loop_int<1, 1, 1>(cctkGH, [&](const Loop::PointDesc &p) {avgdivb_(p.I) = average(divb_, p);});}} // namespace Maxwell
const Loop::GF3D<CCTK_REAL, 0, 1, 1> curlax_(cctkGH, curlax);const Loop::GF3D<CCTK_REAL, 1, 0, 1> curlay_(cctkGH, curlay);const Loop::GF3D<CCTK_REAL, 1, 1, 0> curlaz_(cctkGH, curlaz);
const Loop::GF3D<CCTK_REAL, 0, 1, 1> curlayz_(cctkGH, curlayz);const Loop::GF3D<CCTK_REAL, 1, 0, 1> curlazx_(cctkGH, curlazx);const Loop::GF3D<CCTK_REAL, 1, 1, 0> curlaxy_(cctkGH, curlaxy);
#include <loop.hxx>#include <cctk.h>#include <cctk_Arguments_Checked.h>#include <cctk_Parameters.h>#include <cmath>namespace Maxwell {namespace {template <typename T> T pow2(T x) { return x * x; }template <typename T>T lap(const Loop::GF3D<const T, 1, 1, 1> &var, const Loop::PointDesc &p) {const auto DI = Loop::vect<int, Loop::dim>::unit(0);const auto DJ = Loop::vect<int, Loop::dim>::unit(1);const auto DK = Loop::vect<int, Loop::dim>::unit(2);return fabs(var(p.I - DI) - 2 * var(p.I) + var(p.I + DI)) +fabs(var(p.I - DJ) - 2 * var(p.I) + var(p.I + DJ)) +fabs(var(p.I - DK) - 2 * var(p.I) + var(p.I + DK));}} // namespaceextern "C" void Maxwell_EstimateError(CCTK_ARGUMENTS) {DECLARE_CCTK_ARGUMENTS_Maxwell_EstimateError;DECLARE_CCTK_PARAMETERS;// const Loop::GF3D<const CCTK_REAL, 1, 1, 1> avgphi_(cctkGH, avgphi);// const Loop::GF3D<const CCTK_REAL, 1, 1, 1> avgax_(cctkGH, avgax);// const Loop::GF3D<const CCTK_REAL, 1, 1, 1> avgay_(cctkGH, avgay);// const Loop::GF3D<const CCTK_REAL, 1, 1, 1> avgaz_(cctkGH, avgaz);// const Loop::GF3D<const CCTK_REAL, 1, 1, 1> avgex_(cctkGH, avgex);// const Loop::GF3D<const CCTK_REAL, 1, 1, 1> avgey_(cctkGH, avgey);// const Loop::GF3D<const CCTK_REAL, 1, 1, 1> avgez_(cctkGH, avgez);// const Loop::GF3D<const CCTK_REAL, 1, 1, 1> avgbyz_(cctkGH, avgbyz);// const Loop::GF3D<const CCTK_REAL, 1, 1, 1> avgbzx_(cctkGH, avgbzx);// const Loop::GF3D<const CCTK_REAL, 1, 1, 1> avgbxy_(cctkGH, avgbxy);const Loop::GF3D<CCTK_REAL, 1, 1, 1> regrid_error_(cctkGH, regrid_error);if (false) {// Loop::loop_int<1, 1, 1>(cctkGH, [&](const Loop::PointDesc &p) {// regrid_error_(p.I) = lap(avgphi_, p) + lap(avgax_, p) + lap(avgay_, p)// +// lap(avgaz_, p) + lap(avgex_, p) + lap(avgey_, p) +// lap(avgez_, p) + lap(avgbyz_, p) + lap(avgbzx_, p)// + lap(avgbxy_, p);// });} else if (true) {Loop::loop_int<1, 1, 1>(cctkGH, [&](const Loop::PointDesc &p) {auto r = sqrt(pow2(p.x) + pow2(p.y) + pow2(p.z));regrid_error_(p.I) = 1 / fmax(r, CCTK_REAL(1.0e-10));});} else {assert(0);}}} // namespace Maxwell
#include <loop.hxx>#include <cctk.h>#include <cctk_Arguments_Checked.h>#include <cctk_Parameters.h>namespace Maxwell {extern "C" void Maxwell_EstimateError(CCTK_ARGUMENTS) {DECLARE_CCTK_ARGUMENTS_Maxwell_EstimateError;DECLARE_CCTK_PARAMETERS;const Loop::GF3D<const CCTK_REAL, 0, 0, 0> phi_(cctkGH, phi);const Loop::GF3D<const CCTK_REAL, 1, 0, 0> ax_(cctkGH, ax);const Loop::GF3D<const CCTK_REAL, 0, 1, 0> ay_(cctkGH, ay);const Loop::GF3D<const CCTK_REAL, 0, 0, 1> az_(cctkGH, az);const Loop::GF3D<const CCTK_REAL, 1, 0, 0> ex_(cctkGH, ex);const Loop::GF3D<const CCTK_REAL, 0, 1, 0> ey_(cctkGH, ey);const Loop::GF3D<const CCTK_REAL, 0, 0, 1> ez_(cctkGH, ez);const Loop::GF3D<const CCTK_REAL, 0, 1, 1> byz_(cctkGH, byz);const Loop::GF3D<const CCTK_REAL, 1, 0, 1> bzx_(cctkGH, bzx);const Loop::GF3D<const CCTK_REAL, 1, 1, 0> bxy_(cctkGH, bxy);const Loop::GF3D<CCTK_REAL, 1, 1, 1> regrid_error_(cctkGH, regrid_error);Loop::loop_int<1, 1, 1>(cctkGH, [&](const Loop::PointDesc &p) {const auto diffx = [&](const auto &var_, int i, int j, int k) {CCTK_REAL err = 0;for (int b = 0; b < 2; ++b)for (int a = 0; a < 2; ++a)err += fabs(var_(i + 1, j + a, k + b) - var_(i, j + a, k + b));return err;};const auto diffy = [&](const auto &var_, int i, int j, int k) {CCTK_REAL err = 0;for (int b = 0; b < 2; ++b)for (int a = 0; a < 2; ++a)err += fabs(var_(i + a, j + 1, k + b) - var_(i + a, j, k + b));return err;};const auto diffz = [&](const auto &var_, int i, int j, int k) {CCTK_REAL err = 0;for (int b = 0; b < 2; ++b)for (int a = 0; a < 2; ++a)err += fabs(var_(i + a, j + b, k + 1) - var_(i + a, j + b, k));return err;};const auto diff000 = [&](const auto &var_) {return diffx(var_, p.i, p.j, p.k) + diffy(var_, p.i, p.j, p.k) +diffz(var_, p.i, p.j, p.k);};const auto diff100 = [&](const auto &var_) {return diffx(var_, p.i - 1, p.j, p.k) + diffx(var_, p.i, p.j, p.k) +diffy(var_, p.i, p.j, p.k) + diffz(var_, p.i, p.j, p.k);};const auto diff010 = [&](const auto &var_) {return diffx(var_, p.i, p.j, p.k) + diffy(var_, p.i, p.j - 1, p.k) +diffy(var_, p.i, p.j, p.k) + diffz(var_, p.i, p.j, p.k);};const auto diff001 = [&](const auto &var_) {return diffx(var_, p.i, p.j, p.k) + diffy(var_, p.i, p.j, p.k) +diffz(var_, p.i, p.j, p.k - 1) + diffz(var_, p.i, p.j, p.k);};const auto diff011 = [&](const auto &var_) {return diffx(var_, p.i, p.j, p.k) + diffy(var_, p.i, p.j - 1, p.k) +diffy(var_, p.i, p.j, p.k) + diffz(var_, p.i, p.j, p.k - 1) +diffz(var_, p.i, p.j, p.k);};const auto diff101 = [&](const auto &var_) {return diffx(var_, p.i - 1, p.j, p.k) + diffx(var_, p.i, p.j, p.k) +diffy(var_, p.i, p.j, p.k) + diffz(var_, p.i, p.j, p.k - 1) +diffz(var_, p.i, p.j, p.k);};const auto diff110 = [&](const auto &var_) {return diffx(var_, p.i - 1, p.j, p.k) + diffx(var_, p.i, p.j, p.k) +diffy(var_, p.i, p.j - 1, p.k) + diffy(var_, p.i, p.j, p.k) +diffz(var_, p.i, p.j, p.k);};regrid_error_(p.I) = diff000(phi_) + diff100(ax_) + diff010(ay_) +diff001(az_) + diff100(ex_) + diff010(ey_) +diff001(ez_) + diff011(byz_) + diff101(bzx_) +diff110(bxy_);});}} // namespace Maxwell
template <typename T> struct potential { T phi, ax, ay, az; };
template <typename T> struct potential {// Electric scalar potentialT phi;// Electric vector potential (to ensure div E = 0)T cyz, czx, cxy;// Magnetic vector potentialT ax, ay, az;};
// template <typename F, typename T>// potential<T> calc_dtp(const F &f, T t, T x, T y, T z, T dt) {// auto fm = f(t, x, y, z);// auto fp = f(t + dt, x, y, z);// return {// .phi = (fp.phi - fm.phi) / dt,// .ax = (fp.ax - fm.ax) / dt,// .ay = (fp.ay - fm.ay) / dt,// .az = (fp.az - fm.az) / dt,// };// }
// Continuous derivativetemplate <typename F, typename T>potential<T> calc_dt(const F &f, T t, T x, T y, T z) {auto fd = f(dual<T>(t, 1), dual<T>(x), dual<T>(y), dual<T>(z));return {fd.phi.eps, fd.cyz.eps, fd.czx.eps, fd.cxy.eps,fd.ax.eps, fd.ay.eps, fd.az.eps,};}
};}// template <typename F, typename T>// potential<T> calc_dtm(const F &f, T t, T x, T y, T z, T dt) {// auto fm = f(t - dt, x, y, z);// auto fp = f(t, x, y, z);// return {// .phi = (fp.phi - fm.phi) / dt,// .ax = (fp.ax - fm.ax) / dt,// .ay = (fp.ay - fm.ay) / dt,// .az = (fp.az - fm.az) / dt,// };// }//// template <typename F, typename T>// potential<T> calc_dxm(const F &f, T t, T x, T y, T z, T dx) {// auto fm = f(t, x - dx, y, z);// auto fp = f(t, x, y, z);// return {// .phi = (fp.phi - fm.phi) / dx,// .ax = (fp.ax - fm.ax) / dx,// .ay = (fp.ay - fm.ay) / dx,// .az = (fp.az - fm.az) / dx,// };// }//// template <typename F, typename T>// potential<T> calc_dym(const F &f, T t, T x, T y, T z, T dy) {// auto fm = f(t, x, y - dy, z);// auto fp = f(t, x, y, z);// return {// .phi = (fp.phi - fm.phi) / dy,// .ax = (fp.ax - fm.ax) / dy,// .ay = (fp.ay - fm.ay) / dy,// .az = (fp.az - fm.az) / dy,// };// }//// template <typename F, typename T>// potential<T> calc_dzm(const F &f, T t, T x, T y, T z, T dz) {// auto fm = f(t, x, y, z - dz);// auto fp = f(t, x, y, z);// return {// .phi = (fp.phi - fm.phi) / dz,// .ax = (fp.ax - fm.ax) / dz,// .ay = (fp.ay - fm.ay) / dz,// .az = (fp.az - fm.az) / dz,// };// }template <typename F, typename T>potential<T> calc_dt(const F &f, T t, T x, T y, T z) {auto ff = f(dual<T>(t, 1), dual<T>(x), dual<T>(y), dual<T>(z));return {ff.phi.eps,ff.ax.eps,ff.ay.eps,ff.az.eps,
// template <typename F, typename T>// potential<T> calc_dx(const F &f, T t, T x, T y, T z) {// auto ff = f(dual<T>(t), dual<T>(x, 1), dual<T>(y), dual<T>(z));// return {// ff.phi.eps,// ff.ax.eps,// ff.ay.eps,// ff.az.eps,// };// }//// template <typename F, typename T>// potential<T> calc_dy(const F &f, T t, T x, T y, T z) {// auto ff = f(dual<T>(t), dual<T>(x), dual<T>(y, 1), dual<T>(z));// return {// ff.phi.eps,// ff.ax.eps,// ff.ay.eps,// ff.az.eps,// };// }//// template <typename F, typename T>// potential<T> calc_dz(const F &f, T t, T x, T y, T z) {// auto ff = f(dual<T>(t), dual<T>(x), dual<T>(y), dual<T>(z, 1));// return {// ff.phi.eps,// ff.ax.eps,// ff.ay.eps,// ff.az.eps,// };// }
// choose ht to ensure div E = 0// continuum// T ht =// omega * (hx * kx + hy * ky + hz * kz) / (pow2(kx) + pow2(ky) +// pow2(kz));// discretetypedef complex<T> CT;CT ht =omega *(hx / dx * CT(sin(dx * kx), 2 * pow2(sin(dx * kx / 2))) +hy / dy * CT(sin(dy * ky), 2 * pow2(sin(dy * ky / 2))) +hz / dz * CT(sin(dz * kz), 2 * pow2(sin(dz * kz / 2)))) /CT(4 * ((pow2(sin(dx * kx / 2) / dx)) + (pow2(sin(dy * ky / 2) / dy)) +(pow2(sin(dz * kz / 2) / dz))));CT u = CT(cos(omega * t - kx * x - ky * y - kz * z),sin(omega * t - kx * x - ky * y - kz * z));
assert(hy == 0);assert(hz == 0);// solutionassert(t == 0);T u = sin(omega * t - kz * z);
.phi = real(ht * u),.ax = real(hx * u),.ay = real(hy * u),.az = real(hz * u),};}// Plane wave with Gaussian profiletemplate <typename T> potential<T> gaussian_wave(T t, T x, T y, T z) {DECLARE_CCTK_PARAMETERS;T kx = M_PI * spatial_frequency_x;T ky = M_PI * spatial_frequency_y;T kz = M_PI * spatial_frequency_z;T omega = sqrt(pow2(kx) + pow2(ky) + pow2(kz));T hx = amplitude_x;T hy = amplitude_y;T hz = amplitude_z;T ht =omega * (hx * kx + hy * ky + hz * kz) / (pow2(kx) + pow2(ky) + pow2(kz));T u = exp(-pow2(sin(omega * t - kx * x - ky * y - kz * z) / width) / 2);return {.phi = ht * u,.ax = hx * u,.ay = hy * u,.az = hz * u,
.phi = 0,.cyz = 0,.czx = hx / kz * u,.cxy = 0,.ax = -hx / kz * u,.ay = 0,.az = 0,
loop_setup([&](auto t, auto x, auto y, auto z) {typedef decltype(t) T;return plane_wave(t, x, y, z, T(dx), T(dy), T(dz));});// } else if (CCTK_EQUALS(setup, "Gaussian wave")) {// loop_setup([&](auto t, auto x, auto y, auto z) {// return gaussian_wave(t, x, y, z);// });
loop_setup([&](auto t, auto x, auto y, auto z) { return plane_wave(t, x, y, z); });
#include "dual.hxx"#include <loop.hxx>#include <cctk.h>#include <cctk_Arguments_Checked.h>#include <cctk_Parameters.h>#include <cassert>#include <cmath>#include <complex>namespace Maxwell {using namespace std;namespace {int bitsign(bool s) { return s ? -1 : +1; }template <typename T> T pow2(T x) { return x * x; }template <typename T> T sinc(T x) { return x == T(0) ? T(1) : sin(x) / x; }template <typename T> complex<T> cis(T x) { return {cos(x), sin(x)}; }} // namespace////////////////////////////////////////////////////////////////////////////////template <typename T> struct potential { T phi, ax, ay, az; };// Continuous derivativetemplate <typename F, typename T>potential<T> calc_dt(const F &f, T t, T x, T y, T z) {auto ff = f(dual<T>(t, 1), dual<T>(x), dual<T>(y), dual<T>(z));return {ff.phi.eps,ff.ax.eps,ff.ay.eps,ff.az.eps,};}// Discrete derivativetemplate <typename F, typename T>potential<T> calc_dxc(const F &f, T t, T x, T y, T z, T dx) {auto fm = f(t, x - dx / 2, y, z);auto fp = f(t, x + dx / 2, y, z);return {.phi = (fp.phi - fm.phi) / dx,.ax = (fp.ax - fm.ax) / dx,.ay = (fp.ay - fm.ay) / dx,.az = (fp.az - fm.az) / dx,};}template <typename F, typename T>potential<T> calc_dyc(const F &f, T t, T x, T y, T z, T dy) {auto fm = f(t, x, y - dy / 2, z);auto fp = f(t, x, y + dy / 2, z);return {.phi = (fp.phi - fm.phi) / dy,.ax = (fp.ax - fm.ax) / dy,.ay = (fp.ay - fm.ay) / dy,.az = (fp.az - fm.az) / dy,};}template <typename F, typename T>potential<T> calc_dzc(const F &f, T t, T x, T y, T z, T dz) {auto fm = f(t, x, y, z - dz / 2);auto fp = f(t, x, y, z + dz / 2);return {.phi = (fp.phi - fm.phi) / dz,.ax = (fp.ax - fm.ax) / dz,.ay = (fp.ay - fm.ay) / dz,.az = (fp.az - fm.az) / dz,};}////////////////////////////////////////////////////////////////////////////////// Plane wave implementationtemplate <typename T>potential<complex<T> > plane_wave_impl(T t, T x, T y, T z, T dx, T dy, T dz,T kx, T ky, T kz, T hx, T hy, T hz) {DECLARE_CCTK_PARAMETERS;typedef complex<T> CT;// choose frequency to ensure div E = 0T omega = sqrt(pow2(sinc(kx * dx / 2) * kx) + pow2(sinc(ky * dy / 2) * ky) +pow2(sinc(kz * dz / 2) * kz));// choose amplitude to ensure Lorenz gaugeCT ht = (CT(hx * kx * sinc(kx * dx / 2)) * cis(kx * dx / 2) +CT(hy * ky * sinc(ky * dy / 2)) * cis(ky * dy / 2) +CT(hz * kz * sinc(kz * dz / 2)) * cis(kz * dz / 2)) /CT(omega);CT u = cis(omega * t - kx * x - ky * y - kz * z);return {.phi = ht * u,.ax = hx * u,.ay = hy * u,.az = hz * u,};}// Plane wavetemplate <typename T>potential<T> plane_wave(T t, T x, T y, T z, T dx, T dy, T dz) {DECLARE_CCTK_PARAMETERS;// wave numberT kx = M_PI * spatial_frequency_x;T ky = M_PI * spatial_frequency_y;T kz = M_PI * spatial_frequency_z;// amplitudeT hx = amplitude_x;T hy = amplitude_y;T hz = amplitude_z;//auto p = plane_wave_impl(t, x, y, z, dx, dy, dz, kx, ky, kz, hx, hy, hz);return {.phi = real(p.phi),.ax = real(p.ax),.ay = real(p.ay),.az = real(p.az),};}// Plane wave with a triangle profiletemplate <typename T>potential<T> triangle_wave(T t, T x, T y, T z, T dx, T dy, T dz) {DECLARE_CCTK_PARAMETERS;// wave numberT kx = M_PI * spatial_frequency_x;T ky = M_PI * spatial_frequency_y;T kz = M_PI * spatial_frequency_z;// amplitudeT hx = amplitude_x;T hy = amplitude_y;T hz = amplitude_z;//potential<T> p{0, 0, 0, 0};for (int i = 0; i < num_coefficients; ++i) {const int k = 2 * i + 1;const T kf = k;const T hf = bitsign(i & 1) / pow2(kf);const auto pk = plane_wave_impl(t, x, y, z, dx, dy, dz, kf * kx, kf * ky,kf * kz, hf * hx, hf * hy, hf * hz);p.phi += imag(pk.phi);p.ax += imag(pk.ax);p.ay += imag(pk.ay);p.az += imag(pk.az);}return p;}// Plane wave with Gaussian profile (NOT WORKING)template <typename T> potential<T> gaussian_wave(T t, T x, T y, T z) {DECLARE_CCTK_PARAMETERS;T kx = M_PI * spatial_frequency_x;T ky = M_PI * spatial_frequency_y;T kz = M_PI * spatial_frequency_z;T omega = sqrt(pow2(kx) + pow2(ky) + pow2(kz));T hx = amplitude_x;T hy = amplitude_y;T hz = amplitude_z;T ht =omega * (hx * kx + hy * ky + hz * kz) / (pow2(kx) + pow2(ky) + pow2(kz));T u = exp(-pow2(sin(omega * t - kx * x - ky * y - kz * z) / width) / 2);return {.phi = ht * u,.ax = hx * u,.ay = hy * u,.az = hz * u,};}////////////////////////////////////////////////////////////////////////////////extern "C" void Maxwell_Initial(CCTK_ARGUMENTS) {DECLARE_CCTK_ARGUMENTS_Maxwell_Initial;DECLARE_CCTK_PARAMETERS;const CCTK_REAL t = cctk_time;// const CCTK_REAL dt = CCTK_DELTA_TIME;const CCTK_REAL dx = CCTK_DELTA_SPACE(0);const CCTK_REAL dy = CCTK_DELTA_SPACE(1);const CCTK_REAL dz = CCTK_DELTA_SPACE(2);const Loop::GF3D<CCTK_REAL, 0, 0, 0> phi_(cctkGH, phi);const Loop::GF3D<CCTK_REAL, 1, 0, 0> ax_(cctkGH, ax);const Loop::GF3D<CCTK_REAL, 0, 1, 0> ay_(cctkGH, ay);const Loop::GF3D<CCTK_REAL, 0, 0, 1> az_(cctkGH, az);const Loop::GF3D<CCTK_REAL, 1, 0, 0> ex_(cctkGH, ex);const Loop::GF3D<CCTK_REAL, 0, 1, 0> ey_(cctkGH, ey);const Loop::GF3D<CCTK_REAL, 0, 0, 1> ez_(cctkGH, ez);const Loop::GF3D<CCTK_REAL, 0, 1, 1> byz_(cctkGH, byz);const Loop::GF3D<CCTK_REAL, 1, 0, 1> bzx_(cctkGH, bzx);const Loop::GF3D<CCTK_REAL, 1, 1, 0> bxy_(cctkGH, bxy);const auto loop_setup{[&](const auto &f4) {const auto f{[&](const auto &p) { return f4(t, p.x, p.y, p.z); }};const auto dtf{[&](const auto &p) {return calc_dt([&](auto t, auto x, auto y, auto z) { return f4(t, x, y, z); }, t,p.x, p.y, p.z);}};const auto dxf{[&](const auto &p) {return calc_dxc([&](auto t, auto x, auto y, auto z) { return f4(t, x, y, z); }, t,p.x, p.y, p.z, dx);}};const auto dyf{[&](const auto &p) {return calc_dyc([&](auto t, auto x, auto y, auto z) { return f4(t, x, y, z); }, t,p.x, p.y, p.z, dy);}};const auto dzf{[&](const auto &p) {return calc_dzc([&](auto t, auto x, auto y, auto z) { return f4(t, x, y, z); }, t,p.x, p.y, p.z, dz);}};Loop::loop_int<0, 0, 0>(cctkGH, [&](const Loop::PointDesc &p) { phi_(p.I) = f(p).phi; });Loop::loop_int<1, 0, 0>(cctkGH, [&](const Loop::PointDesc &p) { ax_(p.I) = f(p).ax; });Loop::loop_int<0, 1, 0>(cctkGH, [&](const Loop::PointDesc &p) { ay_(p.I) = f(p).ay; });Loop::loop_int<0, 0, 1>(cctkGH, [&](const Loop::PointDesc &p) { az_(p.I) = f(p).az; });Loop::loop_int<1, 0, 0>(cctkGH, [&](const Loop::PointDesc &p) {ex_(p.I) = -dxf(p).phi - dtf(p).ax;});Loop::loop_int<0, 1, 0>(cctkGH, [&](const Loop::PointDesc &p) {ey_(p.I) = -dyf(p).phi - dtf(p).ay;});Loop::loop_int<0, 0, 1>(cctkGH, [&](const Loop::PointDesc &p) {ez_(p.I) = -dzf(p).phi - dtf(p).az;});Loop::loop_int<0, 1, 1>(cctkGH, [&](const Loop::PointDesc &p) {byz_(p.I) = dyf(p).az - dzf(p).ay;});Loop::loop_int<1, 0, 1>(cctkGH, [&](const Loop::PointDesc &p) {bzx_(p.I) = dzf(p).ax - dxf(p).az;});Loop::loop_int<1, 1, 0>(cctkGH, [&](const Loop::PointDesc &p) {bxy_(p.I) = dxf(p).ay - dyf(p).ax;});}};if (CCTK_EQUALS(setup, "plane wave")) {loop_setup([&](auto t, auto x, auto y, auto z) {typedef decltype(t) T;return plane_wave(t, x, y, z, T(dx), T(dy), T(dz));});} else if (CCTK_EQUALS(setup, "triangle wave")) {loop_setup([&](auto t, auto x, auto y, auto z) {typedef decltype(t) T;return triangle_wave(t, x, y, z, T(dx), T(dy), T(dz));});// } else if (CCTK_EQUALS(setup, "Gaussian wave")) {// loop_setup([&](auto t, auto x, auto y, auto z) {// return gaussian_wave(t, x, y, z);// });} else {assert(0);}}} // namespace Maxwell
#include <loop.hxx>#include <cctk.h>#include <cctk_Arguments_Checked.h>#include <cctk_Parameters.h>namespace Maxwell {extern "C" void Maxwell_Solve(CCTK_ARGUMENTS) { SolvePoisson(); }extern "C" void Maxwell_UpdatePhi(CCTK_ARGUMENTS) {DECLARE_CCTK_ARGUMENTS_Maxwell_UpdatePhi;DECLARE_CCTK_PARAMETERS;const Loop::GF3D<CCTK_REAL, 0, 0, 0> phi_(cctkGH, phi);const Loop::GF3D<const CCTK_REAL, 0, 0, 0> phi1_(cctkGH, phi1);Loop::loop_int<0, 0, 0>(cctkGH, [&](const Loop::PointDesc &p) { phi_(p.I) -= phi1_(p.I); });}} // namespace Maxwell