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