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@@ -1133,7 +1133,7 @@ template <class Real> class Quadrature {
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constexpr Integer KDIM1 = Kernel::TrgDim();
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const Long Nelem = elem_lst.NElem();
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- BuildNbrList(pair_lst, Xt_, trg_surf, elem_lst, 2.5/order_direct, period_length, comm);
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+ BuildNbrList(pair_lst, Xt_, trg_surf, elem_lst, 5.0/order_direct, period_length, comm);
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const Long Ninterac = pair_lst.Dim();
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Vector<Real> Xt;
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@@ -1753,7 +1753,7 @@ template <class Real> class Quadrature {
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Profile::Toc();
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}
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- template <Integer ORDER = 5> static void test(Integer order_singular = 10, Integer order_direct = 5, const Comm& comm = Comm::World()) {
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+ template <Integer ORDER = 10> static void test(Integer order_singular = 20, Integer order_direct = 30, const Comm& comm = Comm::World()) {
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constexpr Integer COORD_DIM = 3;
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constexpr Integer ELEM_DIM = COORD_DIM-1;
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using ElemList = ElemList<COORD_DIM, Basis<Real, ELEM_DIM, ORDER>>;
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@@ -1763,14 +1763,76 @@ template <class Real> class Quadrature {
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int np = comm.Size();
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int rank = comm.Rank();
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auto build_torus = [rank,np](ElemList& elements, long Nt, long Np, Real Rmajor, Real Rminor){
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- auto nodes = ElemList::CoordBasis::Nodes();
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auto torus = [](Real theta, Real phi, Real Rmajor, Real Rminor) {
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- Real R = Rmajor + Rminor * cos<Real>(phi);
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- Real X = R * cos<Real>(theta);
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- Real Y = R * sin<Real>(theta);
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- Real Z = Rminor * sin<Real>(phi);
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+ Real s = Rminor;
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+ Integer Nperiod = 5;
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+ #if 0
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+ Real Aspect_ratio = 10.27932548522949;
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+ Real coeffmat[21][21] = { 0.00000478813217, 0.00000000000000, 0.00000351611652, 0.00000135354389, 0.00000061357832, 0.00000220091101, 0.00000423862912, -0.00003000058678, 0.00000064187111, -0.00024228452821, 0.00003116775770, 0.00000176210710, 0.00000289141326, -0.00000150300525, 0.00000772853855, 0.00000098855242, 0.00000316606793, 0.00000002168364, 0.00000212047939, 0.00000299016097, 0.00000443224508,
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+ 0.00000028202930, 0.00000000000000, -0.00000249222421, -0.00000203136278, 0.00000131104809, 0.00000011987446, -0.00000370760154, 0.00004553918916, -0.00007711342914, -0.00004685295062, 0.00011049838213, -0.00000197486270, 0.00000395827146, 0.00000615046474, 0.00000755337123, 0.00000700606006, 0.00000922725030, -0.00000043310337, 0.00000107416383, 0.00000449787694, 0.00000305137178,
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+ 0.00001226376662, 0.00000000000000, 0.00000270820692, 0.00000208059305, 0.00000521478523, 0.00001779037302, 0.00000846544117, 0.00001120913385, -0.00065816845745, -0.00085107452469, -0.00013171190221, -0.00005540943675, -0.00001835885450, 0.00000101879823, 0.00000209222071, 0.00000091532502, -0.00000521515358, -0.00000209227142, -0.00000678545939, -0.00000034963549, -0.00000015111488,
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+ 0.00001560274177, 0.00000000000000, 0.00000350691471, -0.00001160475040, -0.00001763036562, 0.00003487367940, -0.00002787247831, -0.00000910982726, 0.00008818832430, -0.00524408789352, 0.00009378376126, 0.00004184526188, 0.00002849263365, -0.00002757280527, 0.00003388467667, 0.00000706207265, 0.00000625263419, -0.00003315929280, -0.00001181772132, 0.00000311426015, 0.00001875682574,
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+ -0.00000398287420, 0.00000000000000, -0.00001524541040, 0.00001724056165, 0.00002245173346, 0.00002806861812, -0.00000388776925, 0.00008143573359, -0.00005900909309, 0.00110496615525, 0.00134626252111, 0.00005128383054, -0.00001372421866, 0.00003612563887, 0.00002236580076, -0.00002728391883, 0.00001981237256, 0.00000655450458, 0.00000985319002, 0.00001347597299, 0.00000645987802,
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+ 0.00003304968050, 0.00000000000000, -0.00000530822217, 0.00001324870937, -0.00003610889689, -0.00005478735329, -0.00005818806312, -0.00037112057908, -0.00017812002625, -0.00093204283621, 0.00115969858598, -0.00033559172880, -0.00010441876657, -0.00001617923044, -0.00000555065844, 0.00007343527250, -0.00004408047607, 0.00000403802142, 0.00001843931204, 0.00001694047933, 0.00001213414362,
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+ -0.00000751115658, 0.00000000000000, 0.00005457974839, -0.00000334614515, 0.00005845565465, 0.00015000770509, 0.00021849104087, 0.00002724147635, 0.00167233624961, 0.00011666602222, 0.00276563479565, -0.00085952825611, -0.00030217235326, -0.00008841593808, 0.00000997664119, -0.00015285826521, 0.00002517224675, 0.00003009161810, 0.00001883217556, 0.00002146127554, 0.00001822445302,
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+ -0.00004128706860, 0.00000000000000, -0.00003496417776, 0.00001088761655, -0.00000298955979, -0.00005359326315, -0.00019021633489, -0.00017992728681, -0.00347794801928, 0.00064632791327, 0.00449698418379, -0.00017710507382, 0.00006126180233, 0.00018059254216, 0.00002354096432, 0.00008189838991, -0.00010060678323, -0.00017183290038, 0.00019413756672, 0.00021334811754, 0.00011263617489,
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+ 0.00000853522670, -0.00000000000000, -0.00006544789358, 0.00005424076880, -0.00000679056529, -0.00001249735487, -0.00053082982777, 0.00035396864405, -0.00115020677913, 0.05894451215863, 0.06573092192411, 0.01498018857092, 0.00278125284240, 0.00145188067108, 0.00033717858605, 0.00000800427370, -0.00009335305367, 0.00024286781263, -0.00023916347709, 0.00031213948387, 0.00018134393031,
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+ -0.00002521496390, -0.00000000000000, -0.00054337945767, 0.00012690725271, 0.00053313979879, 0.00064233405283, -0.00047686311882, 0.00176536326762, 0.00074157933705, -0.02684566564858, 1.00000000000000, 0.07176169008017, 0.00837037432939, -0.00000381640211, 0.00088998704450, -0.00049218931235, -0.00024546548957, -0.00036608282244, 0.00049480766756, 0.00031158892671, 0.00006898906577,
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+ 0.00021280418150, 0.00028127161204, -0.00070030166535, 0.00022237010126, -0.00028713891516, -0.00013800295710, 0.00005912094275, 0.00172126013786, -0.00618684850633, 0.03608432412148, Aspect_ratio , 0.49896776676178, 0.00091372377938, -0.00085712829605, -0.00124801427592, -0.00007427225501, -0.00005245858847, 0.00002841771493, 0.00020249813679, -0.00014303345233, 0.00001406490901,
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+ 0.00023699452868, 0.00008661757602, 0.00025744654704, -0.00022715188970, -0.00076146807987, 0.00055185536621, -0.00012325309217, -0.00072356045712, -0.00160693109501, 0.00246682553552, -0.14175094664097, -0.36207047104836, -0.04089594259858, 0.00060774467420, 0.00088646943914, 0.00004865296432, -0.00041878610500, -0.00023025234987, -0.00009676301852, -0.00000000000000, 0.00008409228758,
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+ 0.00011432896281, -0.00000707848403, 0.00004698805787, -0.00043642931269, 0.00081384339137, -0.00065635429928, -0.00011831733718, 0.00017413357273, 0.00224463525228, 0.00478497287259, 0.03294761106372, 0.01078986655921, 0.10731782764196, 0.00075034319889, -0.00009241879889, 0.00055023463210, 0.00006596000458, 0.00005045382932, 0.00014874986664, 0.00000000000000, -0.00015369028552,
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+ 0.00001037383754, 0.00009250180301, 0.00026204055757, 0.00007424291834, -0.00047751804232, 0.00029184055165, 0.00050921301590, -0.00004825839278, -0.00029933769838, 0.00279659987427, 0.00210463814437, -0.00618590926751, -0.02400829829276, -0.02316811867058, -0.00086368201301, -0.00032258985448, -0.00018304496189, 0.00008438774967, -0.00008305341908, 0.00000000000000, 0.00013047417451,
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+ -0.00001376930322, -0.00001723831701, -0.00011543079017, -0.00022646733851, 0.00013467084500, -0.00004661652201, -0.00008419520600, 0.00035772417323, -0.00011815709877, 0.00028718306567, 0.00092207465786, -0.00317224999890, 0.00061770365573, 0.01017294172198, 0.00294739892706, 0.00014669894881, 0.00015702951350, 0.00003432080121, -0.00008555022214, -0.00000000000000, 0.00000454909878,
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+ -0.00000196001542, -0.00003198397462, -0.00004425687075, -0.00004129848094, -0.00003789070615, -0.00027583551127, 0.00025874207495, -0.00002334945384, -0.00007259396807, -0.00008295358566, 0.00011360697681, -0.00101968157105, 0.00046784928418, -0.00208410434425, -0.00313158822246, -0.00046005158219, -0.00010552268213, -0.00005850767775, 0.00003971093611, 0.00000000000000, -0.00005275657168,
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+ -0.00001065901233, -0.00001934838656, -0.00001220186732, -0.00002060524639, -0.00000225423423, -0.00001894621164, -0.00001533334580, -0.00001791087379, 0.00008156246622, -0.00008441298269, 0.00021060956351, -0.00030303673702, 0.00075949780876, -0.00010539998038, 0.00109045265708, 0.00068949378328, 0.00009268362192, 0.00003471063246, 0.00001204656473, -0.00000000000000, 0.00001500743110,
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+ 0.00000105878155, -0.00000910870767, -0.00000172467264, -0.00000722095228, 0.00000699280463, -0.00002061720625, -0.00000889817693, -0.00001993474507, 0.00000370749740, -0.00000090311920, 0.00002677819793, 0.00043428712524, 0.00210293265991, 0.00018200518389, -0.00009621794743, -0.00035250501242, -0.00012996385340, -0.00002185157609, -0.00001116586463, -0.00000000000000, -0.00000451994811,
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+ 0.00000424055270, -0.00000463139304, 0.00000301006116, -0.00000123974939, 0.00000632465435, -0.00002090823000, 0.00001773388794, 0.00000121050368, 0.00001886057362, -0.00001043497195, -0.00002269273500, -0.00021979617304, -0.00001043962493, -0.00116343051195, -0.00004193381756, 0.00007944958634, 0.00007301353617, 0.00002082651736, -0.00000119863023, -0.00000000000000, -0.00001440504820,
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+ -0.00000391270805, -0.00000490489265, -0.00000504441778, -0.00000904507579, -0.00000111389932, 0.00000597532107, 0.00000047090245, -0.00001553130096, -0.00001524566323, -0.00000522222899, -0.00007707672921, -0.00004165665086, 0.00015764687851, 0.00035649110214, 0.00038701237645, 0.00002386798405, -0.00001946414341, -0.00000913835174, -0.00000489907188, 0.00000000000000, 0.00000172327657,
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+ -0.00000015388650, -0.00000603232729, -0.00000397650865, 0.00000280493782, 0.00000463132073, -0.00000788678426, -0.00000471605335, -0.00000283715985, -0.00000422824724, 0.00000366817630, -0.00001159603562, -0.00001625759251, 0.00049116823357, 0.00005048640014, -0.00020234247495, -0.00006341376866, -0.00000807822744, 0.00000070463199, 0.00000014041755, 0.00000000000000, -0.00000718306910};
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+ #else
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+ Real Aspect_ratio = 5;
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+ Real coeffmat[21][21] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 , 0, 0, 0, 0, 0, 0, 0, 0, 0,
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+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 , 0, 0, 0, 0, 0, 0, 0, 0, 0,
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+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 , 0, 0, 0, 0, 0, 0, 0, 0, 0,
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+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 , 0, 0, 0, 0, 0, 0, 0, 0, 0,
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+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 , 0, 0, 0, 0, 0, 0, 0, 0, 0,
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+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 , 0, 0, 0, 0, 0, 0, 0, 0, 0,
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+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 , 0, 0, 0, 0, 0, 0, 0, 0, 0,
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+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 , 0, 0, 0, 0, 0, 0, 0, 0, 0,
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+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 , 0, 0, 0, 0, 0, 0, 0, 0, 0,
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+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, s, 0 , 0, 0, 0, 0, 0, 0, 0, 0, 0,
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+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, Aspect_ratio, 0 , 0, 0, 0, 0, 0, 0, 0, 0, 0,
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+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.2*s, 0, 0, 0, 0, 0, 0, 0, 0, 0,
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+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 , 0, 0, 0, 0, 0, 0, 0, 0, 0,
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+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 , 0, 0, 0, 0, 0, 0, 0, 0, 0,
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+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 , 0, 0, 0, 0, 0, 0, 0, 0, 0,
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+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 , 0, 0, 0, 0, 0, 0, 0, 0, 0,
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+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 , 0, 0, 0, 0, 0, 0, 0, 0, 0,
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+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 , 0, 0, 0, 0, 0, 0, 0, 0, 0,
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+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 , 0, 0, 0, 0, 0, 0, 0, 0, 0,
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+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 , 0, 0, 0, 0, 0, 0, 0, 0, 0,
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+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 , 0, 0, 0, 0, 0, 0, 0, 0, 0};
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+ #endif
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+ Real Z = 0;
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+ Real R = 0;
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+ for (long i = -10; i <= 10; i++) {
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+ for (long j = -10; j <= 10; j++) {
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+ R += coeffmat[i+10][j+10] * cos(-i*phi + Nperiod*j*theta)*Rmajor;
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+ Z += coeffmat[i+10][j+10] * sin(-i*phi + Nperiod*j*theta)*Rmajor;
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+ }
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+ }
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+ Real X = R * cos(theta);
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+ Real Y = R * sin(theta);
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return std::make_tuple(X,Y,Z);
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};
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+ //auto torus = [](Real theta, Real phi, Real Rmajor, Real Rminor) {
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+ // Real R = Rmajor + Rminor * cos<Real>(phi);
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+ // Real X = R * cos<Real>(theta);
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+ // Real Y = R * sin<Real>(theta);
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+ // Real Z = Rminor * sin<Real>(phi);
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+ // return std::make_tuple(X,Y,Z);
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+ //};
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+ auto nodes = ElemList::CoordBasis::Nodes();
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long start = Nt*Np*(rank+0)/np;
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long end = Nt*Np*(rank+1)/np;
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@@ -1790,8 +1852,8 @@ template <class Real> class Quadrature {
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}
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};
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ElemList elements_src, elements_trg;
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- build_torus(elements_src, 28, 16, 2, 1.0);
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- build_torus(elements_trg, 29, 17, 2, 0.99);
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+ build_torus(elements_src, 60, 12, 2, 1.0);
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+ build_torus(elements_trg, 61, 13, 2, 0.99);
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Vector<Real> Xt;
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Vector<PotentialBasis> U_onsurf, U_offsurf;
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@@ -5737,8 +5799,8 @@ template <class Real, Integer ORDER=10> class MHDEquilib {
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long Np = fft_r2c.Dim(1) / (Nt * 2);
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SCTL_ASSERT(fft_r2c.Dim(1) == Nt * Np * 2);
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- auto filter_fn = [](Real x2, Real sigma) {return exp(-x2/(2*sigma*sigma));};
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- //auto filter_fn = [](Real x2, Real sigma) {return (x2<sigma*sigma?1.0:0.0);};
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+ //auto filter_fn = [](Real x2, Real sigma) {return exp(-x2/(2*sigma*sigma));};
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+ auto filter_fn = [](Real x2, Real sigma) {return (x2<sigma*sigma?1.0:0.0);};
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Vector<Real> coeff(fft_r2c.Dim(1));
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for (long k = 0; k < dof; k++) {
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@@ -6357,7 +6419,7 @@ template <class Real, Integer ORDER=10> class MHDEquilib {
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pressure_ = pressure;
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flux_tor_ = flux_tor;
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flux_pol_ = flux_pol;
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- iter = 57;
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+ iter = 0;
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}
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Real operator()(const Eigen::VectorXd& x, Eigen::VectorXd& grad_direction, Eigen::VectorXd* grad_op_ptr = nullptr) {
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@@ -6441,9 +6503,6 @@ template <class Real, Integer ORDER=10> class MHDEquilib {
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grad_direction_orig_.ReInit(x.size());
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Vector<Real> dgdnu_fourier = cheb2grid(S_, dgdnu);
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for (Long i = 0; i < S_.Nsurf(); i++) { // Init grad_direction_, make it divergence-free, filter
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- const Long Mt = S_.NTor(i);
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- const Long Mp = S_.NPol(i);
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- const Long offset = S_.ElemDsp(i);
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const Long Nt = fourier_dim0;
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const Long Np = fourier_dim1;
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@@ -6473,32 +6532,37 @@ template <class Real, Integer ORDER=10> class MHDEquilib {
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Sop.GradInvSurfLap(GradInvLapF, dX, d2X, F, 1e-8, 100, 1.0);
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for (Long j = 0; j < Nt*Np; j++) { // grad_direction <-- normal * dgdnu - GradInvLapF
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- grad_direction[0*Nt*Np+j] = normal[0*Nt*Np+j] * dgdnu[j] - GradInvLapF[0*Nt*Np+j]*0;
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- grad_direction[1*Nt*Np+j] = normal[1*Nt*Np+j] * dgdnu[j] - GradInvLapF[1*Nt*Np+j]*0;
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- grad_direction[2*Nt*Np+j] = normal[2*Nt*Np+j] * dgdnu[j] - GradInvLapF[2*Nt*Np+j]*0;
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+ grad_direction[0*Nt*Np+j] = normal[0*Nt*Np+j] * dgdnu[j] - GradInvLapF[0*Nt*Np+j];
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+ grad_direction[1*Nt*Np+j] = normal[1*Nt*Np+j] * dgdnu[j] - GradInvLapF[1*Nt*Np+j];
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+ grad_direction[2*Nt*Np+j] = normal[2*Nt*Np+j] * dgdnu[j] - GradInvLapF[2*Nt*Np+j];
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}
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{ ////////////////////
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Vector<Real> grad_direction_orig(COORD_DIM*Nt*Np, (Iterator<Real>)grad_direction_orig_.begin() + COORD_DIM*i * (fourier_dim0*fourier_dim1), false);
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- grad_direction_orig = grad_direction;
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+ //grad_direction_orig = grad_direction;
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+ for (Long j = 0; j < Nt*Np; j++) { // grad_direction <-- normal * dgdnu - GradInvLapF
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+ grad_direction_orig[0*Nt*Np+j] = normal[0*Nt*Np+j] * dgdnu[j] - GradInvLapF[0*Nt*Np+j]*0;
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+ grad_direction_orig[1*Nt*Np+j] = normal[1*Nt*Np+j] * dgdnu[j] - GradInvLapF[1*Nt*Np+j]*0;
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+ grad_direction_orig[2*Nt*Np+j] = normal[2*Nt*Np+j] * dgdnu[j] - GradInvLapF[2*Nt*Np+j]*0;
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+ }
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}
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- fourier_filter(grad_direction, Nt, Np, 2);
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+ fourier_filter(grad_direction, Nt, Np, S_.NPol(i)*1.2);
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for (Long k = 0; k < 50; k++) { // reparameterize
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Real max_resid = 0;
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Vector<Real> correction(COORD_DIM*Nt*Np);
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- for (Long i = 0; i < Nt*Np; i++) { // Set correction
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- Real resid = dgdnu[i];
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- resid -= normal[0*Nt*Np+i] * grad_direction[0*Nt*Np+i];
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- resid -= normal[1*Nt*Np+i] * grad_direction[1*Nt*Np+i];
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- resid -= normal[2*Nt*Np+i] * grad_direction[2*Nt*Np+i];
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+ for (Long j = 0; j < Nt*Np; j++) { // Set correction
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+ Real resid = dgdnu[j];
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+ resid -= normal[0*Nt*Np+j] * grad_direction[0*Nt*Np+j];
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+ resid -= normal[1*Nt*Np+j] * grad_direction[1*Nt*Np+j];
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+ resid -= normal[2*Nt*Np+j] * grad_direction[2*Nt*Np+j];
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max_resid = std::max(max_resid, fabs(resid));
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- correction[0*Nt*Np+i] = normal[0*Nt*Np+i] * resid;
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- correction[1*Nt*Np+i] = normal[1*Nt*Np+i] * resid;
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- correction[2*Nt*Np+i] = normal[2*Nt*Np+i] * resid;
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+ correction[0*Nt*Np+j] = normal[0*Nt*Np+j] * resid;
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+ correction[1*Nt*Np+j] = normal[1*Nt*Np+j] * resid;
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+ correction[2*Nt*Np+j] = normal[2*Nt*Np+j] * resid;
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}
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std::cout<<max_resid<<' '; //////////////////////////////////
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- fourier_filter(correction, Nt, Np, 2);
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+ fourier_filter(correction, Nt, Np, S_.NPol(i)*1.2);
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Real alpha = 0;
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{ // Set alpha <-- (dgdnu - x.n, c.n) / (c.n, c.n)
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@@ -6597,8 +6661,8 @@ template <class Real, Integer ORDER=10> class MHDEquilib {
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X[i*COORD_DIM+2] = mhd_equilib.S_.Elem(i,2);
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}
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Vector<Real> X_fourier = cheb2grid(mhd_equilib.S_, X);
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+ //X_fourier.Read(("X"+std::to_string(mhd_equilib.iter)+"_").c_str()); // Read from file
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x.resize(X_fourier.Dim());
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- X_fourier.Read(("X"+std::to_string(mhd_equilib.iter)+"_").c_str()); // Read from file
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for (Long i = 0; i < X_fourier.Dim(); i++) {
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x(i) = X_fourier[i];
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}
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@@ -6631,8 +6695,8 @@ template <class Real, Integer ORDER=10> class MHDEquilib {
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{ // Init S, flux_tor, flux_pol, pressure
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Vector<Long> NtNp;
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for (Long i = 0; i < Nsurf; i++) {
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- NtNp.PushBack(70);
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- NtNp.PushBack(14);
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+ NtNp.PushBack(35);
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+ NtNp.PushBack(7);
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//NtNp.PushBack(30);
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//NtNp.PushBack(4);
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}
|
