1 #pragma once 2 3 #define LANDAU_INVSQRT(q) (1. / PetscSqrtReal(q)) 4 5 #if defined(__CUDA_ARCH__) 6 #define PETSC_DEVICE_FUNC_DECL __device__ 7 #elif defined(KOKKOS_INLINE_FUNCTION) 8 #define PETSC_DEVICE_FUNC_DECL KOKKOS_INLINE_FUNCTION 9 #else 10 #define PETSC_DEVICE_FUNC_DECL 11 #endif 12 13 #if LANDAU_DIM == 2 14 /* elliptic functions 15 */ 16 PETSC_DEVICE_FUNC_DECL static PetscReal polevl_10(PetscReal x, const PetscReal coef[]) 17 { 18 PetscReal ans; 19 PetscInt i; 20 ans = coef[0]; 21 for (i = 1; i < 11; i++) ans = ans * x + coef[i]; 22 return ans; 23 } 24 PETSC_DEVICE_FUNC_DECL static PetscReal polevl_9(PetscReal x, const PetscReal coef[]) 25 { 26 PetscReal ans; 27 PetscInt i; 28 ans = coef[0]; 29 for (i = 1; i < 10; i++) ans = ans * x + coef[i]; 30 return ans; 31 } 32 /* 33 * Complete elliptic integral of the second kind 34 */ 35 PETSC_DEVICE_FUNC_DECL static void ellipticE(PetscReal x, PetscReal *ret) 36 { 37 #if defined(PETSC_USE_REAL_SINGLE) 38 static const PetscReal P2[] = {1.53552577301013293365E-4F, 2.50888492163602060990E-3F, 8.68786816565889628429E-3F, 1.07350949056076193403E-2F, 7.77395492516787092951E-3F, 7.58395289413514708519E-3F, 39 1.15688436810574127319E-2F, 2.18317996015557253103E-2F, 5.68051945617860553470E-2F, 4.43147180560990850618E-1F, 1.00000000000000000299E0F}; 40 static const PetscReal Q2[] = {3.27954898576485872656E-5F, 1.00962792679356715133E-3F, 6.50609489976927491433E-3F, 1.68862163993311317300E-2F, 2.61769742454493659583E-2F, 41 3.34833904888224918614E-2F, 4.27180926518931511717E-2F, 5.85936634471101055642E-2F, 9.37499997197644278445E-2F, 2.49999999999888314361E-1F}; 42 #else 43 static const PetscReal P2[] = {1.53552577301013293365E-4, 2.50888492163602060990E-3, 8.68786816565889628429E-3, 1.07350949056076193403E-2, 7.77395492516787092951E-3, 7.58395289413514708519E-3, 44 1.15688436810574127319E-2, 2.18317996015557253103E-2, 5.68051945617860553470E-2, 4.43147180560990850618E-1, 1.00000000000000000299E0}; 45 static const PetscReal Q2[] = {3.27954898576485872656E-5, 1.00962792679356715133E-3, 6.50609489976927491433E-3, 1.68862163993311317300E-2, 2.61769742454493659583E-2, 46 3.34833904888224918614E-2, 4.27180926518931511717E-2, 5.85936634471101055642E-2, 9.37499997197644278445E-2, 2.49999999999888314361E-1}; 47 #endif 48 x = 1 - x; /* where m = 1 - m1 */ 49 *ret = polevl_10(x, P2) - PetscLogReal(x) * (x * polevl_9(x, Q2)); 50 } 51 /* 52 * Complete elliptic integral of the first kind 53 */ 54 PETSC_DEVICE_FUNC_DECL static void ellipticK(PetscReal x, PetscReal *ret) 55 { 56 #if defined(PETSC_USE_REAL_SINGLE) 57 static const PetscReal P1[] = {1.37982864606273237150E-4F, 2.28025724005875567385E-3F, 7.97404013220415179367E-3F, 9.85821379021226008714E-3F, 6.87489687449949877925E-3F, 6.18901033637687613229E-3F, 58 8.79078273952743772254E-3F, 1.49380448916805252718E-2F, 3.08851465246711995998E-2F, 9.65735902811690126535E-2F, 1.38629436111989062502E0F}; 59 static const PetscReal Q1[] = {2.94078955048598507511E-5F, 9.14184723865917226571E-4F, 5.94058303753167793257E-3F, 1.54850516649762399335E-2F, 2.39089602715924892727E-2F, 3.01204715227604046988E-2F, 60 3.73774314173823228969E-2F, 4.88280347570998239232E-2F, 7.03124996963957469739E-2F, 1.24999999999870820058E-1F, 4.99999999999999999821E-1F}; 61 #else 62 static const PetscReal P1[] = {1.37982864606273237150E-4, 2.28025724005875567385E-3, 7.97404013220415179367E-3, 9.85821379021226008714E-3, 6.87489687449949877925E-3, 6.18901033637687613229E-3, 63 8.79078273952743772254E-3, 1.49380448916805252718E-2, 3.08851465246711995998E-2, 9.65735902811690126535E-2, 1.38629436111989062502E0}; 64 static const PetscReal Q1[] = {2.94078955048598507511E-5, 9.14184723865917226571E-4, 5.94058303753167793257E-3, 1.54850516649762399335E-2, 2.39089602715924892727E-2, 3.01204715227604046988E-2, 65 3.73774314173823228969E-2, 4.88280347570998239232E-2, 7.03124996963957469739E-2, 1.24999999999870820058E-1, 4.99999999999999999821E-1}; 66 #endif 67 x = 1 - x; /* where m = 1 - m1 */ 68 *ret = polevl_10(x, P1) - PetscLogReal(x) * polevl_10(x, Q1); 69 } 70 /* flip sign. papers use du/dt = C, PETSc uses form G(u) = du/dt - C(u) = 0 */ 71 PETSC_DEVICE_FUNC_DECL static void LandauTensor2D(const PetscReal x[], const PetscReal rp, const PetscReal zp, PetscReal Ud[][2], PetscReal Uk[][2], const PetscReal mask) 72 { 73 PetscReal l, s, r = x[0], z = x[1], i1func, i2func, i3func, ks, es, pi4pow, sqrt_1s, r2, rp2, r2prp2, zmzp, zmzp2, tt; 74 //PetscReal mask /* = !!(r!=rp || z!=zp) */; 75 /* !!(zmzp2 > 1.e-12 || (r-rp) > 1.e-12 || (r-rp) < -1.e-12); */ 76 r2 = PetscSqr(r); 77 zmzp = z - zp; 78 rp2 = PetscSqr(rp); 79 zmzp2 = PetscSqr(zmzp); 80 r2prp2 = r2 + rp2; 81 l = r2 + rp2 + zmzp2; 82 /* if (zmzp2 > PETSC_SMALL) mask = 1; */ 83 /* else if ((tt=(r-rp)) > PETSC_SMALL) mask = 1; */ 84 /* else if (tt < -PETSC_SMALL) mask = 1; */ 85 /* else mask = 0; */ 86 s = mask * 2 * r * rp / l; /* mask for vectorization */ 87 tt = 1. / (1 + s); 88 pi4pow = 4 * PETSC_PI * LANDAU_INVSQRT(PetscSqr(l) * l); 89 sqrt_1s = PetscSqrtReal(1. + s); 90 /* sp.ellipe(2.*s/(1.+s)) */ 91 ellipticE(2 * s * tt, &es); /* 44 flops * 2 + 75 = 163 flops including 2 logs, 1 sqrt, 1 pow, 21 mult */ 92 /* sp.ellipk(2.*s/(1.+s)) */ 93 ellipticK(2 * s * tt, &ks); /* 44 flops + 75 in rest, 21 mult */ 94 /* mask is needed here just for single precision */ 95 i2func = 2. / ((1 - s) * sqrt_1s) * es; 96 i1func = 4. / (PetscSqr(s) * sqrt_1s + PETSC_MACHINE_EPSILON) * mask * (ks - (1. + s) * es); 97 i3func = 2. / ((1 - s) * (s)*sqrt_1s + PETSC_MACHINE_EPSILON) * (es - (1 - s) * ks); 98 Ud[0][0] = -pi4pow * (rp2 * i1func + PetscSqr(zmzp) * i2func); 99 Ud[0][1] = Ud[1][0] = Uk[0][1] = pi4pow * (zmzp) * (r * i2func - rp * i3func); 100 Uk[1][1] = Ud[1][1] = -pi4pow * ((r2prp2)*i2func - 2 * r * rp * i3func) * mask; 101 Uk[0][0] = -pi4pow * (zmzp2 * i3func + r * rp * i1func); 102 Uk[1][0] = pi4pow * (zmzp) * (r * i3func - rp * i2func); /* 48 mults + 21 + 21 = 90 mults and divs */ 103 } 104 #else 105 /* integration point functions */ 106 /* Evaluates the tensor U=(I-(x-y)(x-y)/(x-y)^2)/|x-y| at point x,y */ 107 /* if x==y we will return zero. This is not the correct result */ 108 /* since the tensor diverges for x==y but when integrated */ 109 /* the divergent part is antisymmetric and vanishes. This is not */ 110 /* trivial, but can be proven. */ 111 static PETSC_DEVICE_FUNC_DECL void LandauTensor3D(const PetscReal x1[], const PetscReal xp, const PetscReal yp, const PetscReal zp, PetscReal U[][3], PetscReal mask) 112 { 113 PetscReal dx[3], inorm3, inorm, inorm2, norm2, x2[] = {xp, yp, zp}; 114 PetscInt d; 115 for (d = 0, norm2 = PETSC_MACHINE_EPSILON; d < 3; ++d) { 116 dx[d] = x2[d] - x1[d]; 117 norm2 += dx[d] * dx[d]; 118 } 119 inorm2 = mask / norm2; 120 inorm = PetscSqrtReal(inorm2); 121 inorm3 = inorm2 * inorm; 122 for (d = 0; d < 3; ++d) U[d][d] = -(inorm - inorm3 * dx[d] * dx[d]); 123 U[1][0] = U[0][1] = inorm3 * dx[0] * dx[1]; 124 U[1][2] = U[2][1] = inorm3 * dx[2] * dx[1]; 125 U[2][0] = U[0][2] = inorm3 * dx[0] * dx[2]; 126 } 127 /* Relativistic form */ 128 #define GAMMA3(_x, _c02) PetscSqrtReal(1.0 + ((_x[0] * _x[0]) + (_x[1] * _x[1]) + (_x[2] * _x[2])) / (_c02)) 129 static PETSC_DEVICE_FUNC_DECL void LandauTensor3DRelativistic(const PetscReal a_x1[], const PetscReal xp, const PetscReal yp, const PetscReal zp, PetscReal U[][3], PetscReal mask, PetscReal c0) 130 { 131 const PetscReal x2[3] = {xp, yp, zp}, x1[3] = {a_x1[0], a_x1[1], a_x1[2]}, c02 = c0 * c0, g1 = GAMMA3(x1, c02), g2 = GAMMA3(x2, c02); 132 PetscReal fact, u1u2, diff[3], udiff2, u12, u22, wsq, rsq, tt; 133 PetscInt i, j; 134 135 if (mask == 0.0) { 136 for (i = 0; i < 3; ++i) { 137 for (j = 0; j < 3; ++j) U[i][j] = 0; 138 } 139 } else { 140 for (i = 0, u1u2 = u12 = u22 = udiff2 = 0; i < 3; ++i) { 141 diff[i] = x1[i] - x2[i]; 142 udiff2 += diff[i] * diff[i]; 143 u12 += x1[i] * x1[i]; 144 u22 += x2[i] * x2[i]; 145 u1u2 += x1[i] * x2[i]; 146 } 147 tt = 2. * u1u2 * (1. - g1 * g2) + (u12 * u22 + u1u2 * u1u2) / c02; // these two terms are about the same with opposite sign 148 wsq = udiff2 + tt; 149 //wsq = udiff2 + 2.*u1u2*(1.-g1*g2) + (u12*u22 + u1u2*u1u2)/c02; 150 rsq = 1. + wsq / c02; 151 fact = -rsq / (g1 * g2 * PetscSqrtReal(wsq)); /* flip sign. papers use du/dt = C, PETSc uses form G(u) = du/dt - C(u) = 0 */ 152 for (i = 0; i < 3; ++i) { 153 for (j = 0; j < 3; ++j) U[i][j] = fact * (-diff[i] * diff[j] / wsq + (PetscSqrtReal(rsq) - 1.) * (x1[i] * x2[j] + x1[j] * x2[i]) / wsq); 154 U[i][i] += fact; 155 } 156 } 157 } 158 159 #endif 160