l1, l2, l3, l4, eta = symbols('lambda[0] lambda[1] lambda[2] lambda[3] eta') lf0, lf1 = symbols('lambda_f[0] lambda_f[1]') # Additional parameters for damping term R0 = symbols('BSSN_ETA_R0') ep1, ep2 = symbols('BSSN_ETA_POWER[0] BSSN_ETA_POWER[1]') xi1, xi2, xi3 = symbols('BSSN_XI[0] BSSN_XI[1] BSSN_XI[2] ') # declare variables a = dendro.scalar("alpha", "[pp]") chi = dendro.scalar("chi", "[pp]") K = dendro.scalar("K", "[pp]") Gt = dendro.vec3("Gt", "[pp]") b = dendro.vec3("beta", "[pp]") B = dendro.vec3("B", "[pp]") gt = dendro.sym_3x3("gt", "[pp]") At = dendro.sym_3x3("At", "[pp]") Gt_rhs = dendro.vec3("Gt_rhs", "[pp]") # Lie derivative weight weight = -Rational(2, 3) weight_Gt = Rational(2, 3) # specify the functions for computing first and second derivatives d = dendro.set_first_derivative('grad') # first argument is direction
def bssn_puncture_gauge(eta_damp, isStaged=False, prefix=""): if (not isStaged): C1 = dendro.get_first_christoffel() C2 = dendro.get_second_christoffel() C2_spatial = dendro.get_complete_christoffel(chi) [R, Rt, Rphi, CalGt] = dendro.compute_ricci(Gt, chi) a_rhs = l1 * dendro.lie(b, a) - 2 * a * K b_rhs = [(Rational(3, 4) * (lf0 + lf1 * a) * B[i] + l2 * dendro.vec_j_ad_j(b, b[i])) for i in dendro.e_i] gt_rhs = dendro.lie(b, gt, weight) - 2 * a * At chi_rhs = dendro.lie(b, chi, weight) + Rational(2, 3) * (chi * a * K) AikAkj = Matrix([ sum([ At[i, k] * sum([dendro.inv_metric[k, l] * At[l, j] for l in dendro.e_i]) for k in dendro.e_i ]) for i, j in dendro.e_ij ]) At_rhs = dendro.lie(b, At, weight) + chi * dendro.trace_free( a * R - dendro.DiDj(a)) + a * (K * At - 2 * AikAkj.reshape(3, 3)) K_rhs = dendro.lie(b, K) - dendro.laplacian( a, chi) + a * (K * K / 3 + dendro.sqr(At)) At_UU = dendro.up_up(At) Gt_rhs = Matrix([sum(b[j]*ad(j,Gt[i]) for j in dendro.e_i) for i in dendro.e_i]) - \ Matrix([sum(CalGt[j]*d(j,b[i]) for j in dendro.e_i) for i in dendro.e_i]) + \ Rational(2,3)*Matrix([ CalGt[i] * sum(d(j,b[j]) for j in dendro.e_i) for i in dendro.e_i ]) + \ Matrix([sum([igt[j, k] * d2(j, k, b[i]) + igt[i, j] * d2(j, k, b[k])/3 for j, k in dendro.e_ij]) for i in dendro.e_i]) - \ Matrix([sum([2*At_UU[i, j]*d(j, a) for j in dendro.e_i]) for i in dendro.e_i]) + \ Matrix([sum([2*a*dendro.C2[i, j, k]*At_UU[j, k] for j,k in dendro.e_ij]) for i in dendro.e_i]) - \ Matrix([sum([a*(3/chi*At_UU[i,j]*d(j, chi) + Rational(4,3)*dendro.inv_metric[i, j]*d(j, K)) for j in dendro.e_i]) for i in dendro.e_i]) Gt_rhs = [item for sublist in Gt_rhs.tolist() for item in sublist] B_rhs = [ (Gt_rhs[i] - eta_damp * B[i] + l3 * dendro.vec_j_ad_j(b, B[i]) - l4 * dendro.vec_j_ad_j(b, Gt[i])) for i in dendro.e_i ] ################################################################### # generate code ################################################################### outs = [a_rhs, b_rhs, gt_rhs, chi_rhs, At_rhs, K_rhs, Gt_rhs, B_rhs] vnames = [ 'a_rhs', 'b_rhs', 'gt_rhs', 'chi_rhs', 'At_rhs', 'K_rhs', 'Gt_rhs', 'B_rhs' ] dendro.generate_cpu(outs, vnames, '[pp]') else: # note: these are just the symbolic vars that is being used to generate the # Gt_rhs by satges _Gt_rhs_s1 = dendro.vec3("Gt_rhs_s1_", "[pp]") _Gt_rhs_s2 = dendro.vec3("Gt_rhs_s2_", "[pp]") _Gt_rhs_s3 = dendro.vec3("Gt_rhs_s3_", "[pp]") _Gt_rhs_s4 = dendro.vec3("Gt_rhs_s4_", "[pp]") _Gt_rhs_s5 = dendro.vec3("Gt_rhs_s5_", "[pp]") _Gt_rhs_s6 = dendro.vec3("Gt_rhs_s6_", "[pp]") _Gt_rhs_s7 = dendro.vec3("Gt_rhs_s7_", "[pp]") _CalGt = dendro.vec3("CalGt", "[pp]") _Gt_rhs = dendro.vec3("Gt_rhs", "[pp]") # Gt_rhs staged vars that is being used to generate the code. At_UU = dendro.sym_3x3("At_UU", "[pp]") CalGt = dendro.vec3("CalGt", "[pp]") Gt_rhs_s1 = dendro.vec3("Gt_rhs_s1_", "[pp]") Gt_rhs_s2 = dendro.vec3("Gt_rhs_s2_", "[pp]") Gt_rhs_s3 = dendro.vec3("Gt_rhs_s3_", "[pp]") Gt_rhs_s4 = dendro.vec3("Gt_rhs_s4_", "[pp]") Gt_rhs_s5 = dendro.vec3("Gt_rhs_s5_", "[pp]") Gt_rhs_s6 = dendro.vec3("Gt_rhs_s6_", "[pp]") Gt_rhs_s7 = dendro.vec3("Gt_rhs_s7_", "[pp]") C1 = dendro.get_first_christoffel() C2 = dendro.get_second_christoffel() C2_spatial = dendro.get_complete_christoffel(chi) [R, Rt, Rphi, CalGt] = dendro.compute_ricci(Gt, chi) a_rhs = l1 * dendro.lie(b, a) - 2 * a * K b_rhs = [(Rational(3, 4) * (lf0 + lf1 * a) * B[i] + l2 * dendro.vec_j_ad_j(b, b[i])) for i in dendro.e_i] gt_rhs = dendro.lie(b, gt, weight) - 2 * a * At chi_rhs = dendro.lie(b, chi, weight) + Rational(2, 3) * (chi * a * K) AikAkj = Matrix([ sum([ At[i, k] * sum([dendro.inv_metric[k, l] * At[l, j] for l in dendro.e_i]) for k in dendro.e_i ]) for i, j in dendro.e_ij ]) At_rhs = dendro.lie(b, At, weight) + chi * dendro.trace_free( a * R - dendro.DiDj(a)) + a * (K * At - 2 * AikAkj.reshape(3, 3)) K_rhs = dendro.lie(b, K) - dendro.laplacian( a, chi) + a * (K * K / 3 + dendro.sqr(At)) At_UU = dendro.up_up(At) Gt_rhs_s1 = ([ sum(b[j] * ad(j, Gt[i]) for j in dendro.e_i) for i in dendro.e_i ]) Gt_rhs_s2 = ([ sum(_CalGt[j] * d(j, b[i]) for j in dendro.e_i) for i in dendro.e_i ]) Gt_rhs_s3 = ([ _CalGt[i] * sum(d(j, b[j]) for j in dendro.e_i) for i in dendro.e_i ]) Gt_rhs_s4 = ([ sum([ igt[j, k] * d2(j, k, b[i]) + igt[i, j] * d2(j, k, b[k]) / 3 for j, k in dendro.e_ij ]) for i in dendro.e_i ]) Gt_rhs_s5 = ([ sum([2 * At_UU[i, j] * d(j, a) for j in dendro.e_i]) for i in dendro.e_i ]) Gt_rhs_s6 = ([ sum([ 2 * a * dendro.C2[i, j, k] * At_UU[j, k] for j, k in dendro.e_ij ]) for i in dendro.e_i ]) Gt_rhs_s7 = ([ sum([ a * (3 / chi * At_UU[i, j] * d(j, chi) + Rational(4, 3) * dendro.inv_metric[i, j] * d(j, K)) for j in dendro.e_i ]) for i in dendro.e_i ]) Gt_rhs = Matrix(_Gt_rhs_s1) - \ Matrix(_Gt_rhs_s2) + \ Rational(2,3)*Matrix(_Gt_rhs_s3) + \ Matrix(_Gt_rhs_s4) - \ Matrix(_Gt_rhs_s5) + \ Matrix(_Gt_rhs_s6) - \ Matrix(_Gt_rhs_s7) Gt_rhs = [item for sublist in Gt_rhs.tolist() for item in sublist] B_rhs = [ (Gt_rhs[i] - eta_damp * B[i] + l3 * dendro.vec_j_ad_j(b, B[i]) - l4 * dendro.vec_j_ad_j(b, Gt[i])) for i in dendro.e_i ] outs = [ a_rhs, b_rhs, gt_rhs, chi_rhs, At_rhs, K_rhs, CalGt, Gt_rhs_s1, Gt_rhs_s2, Gt_rhs_s3, Gt_rhs_s4, Gt_rhs_s5, Gt_rhs_s6, Gt_rhs_s7, Gt_rhs, B_rhs ] vnames = [ 'a_rhs', 'b_rhs', 'gt_rhs', 'chi_rhs', 'At_rhs', 'K_rhs', 'CalGt', 'Gt_rhs_s1_', 'Gt_rhs_s2_', 'Gt_rhs_s3_', 'Gt_rhs_s4_', 'Gt_rhs_s5_', 'Gt_rhs_s6_', 'Gt_rhs_s7_', 'Gt_rhs', 'B_rhs' ] ################################################################### # generate code ################################################################### numVars = len(outs) for i in range(0, numVars): dendro.generate_separate([outs[i]], [vnames[i]], '[pp]')
#!/usr/bin/env/ python3 import dendro from sympy import * ################################################################### # initialize ################################################################### # Declare variables. # These include the BSSN variables that we need for the Psi4 # calculation. chi = dendro.scalar("chi", "[pp]") K = dendro.scalar("K", "[pp]") Gt = dendro.vec3("Gt", "[pp]") gt = dendro.sym_3x3("gt", "[pp]") At = dendro.sym_3x3("At", "[pp]") # Specify the operators needed for computing first and second derivatives d = dendro.set_first_derivative('grad') # first argument is direction d2 = dendro.set_second_derivative('grad2') # first 2 arguments are directions ad = dendro.set_advective_derivative('agrad') # first argument is direction # Metric related quantities, i.e. the metric and its inverse dendro.set_metric(gt) igt = dendro.get_inverse_metric() # Christoffels, Ricci, et al C1 = dendro.get_first_christoffel() C2 = dendro.get_second_christoffel()
from sympy import * from sympy.physics.vector.vector import Vector from sympy.printing.dot import dotprint ################################################################### # initialize ################################################################### l1, l2, l3, l4, eta = symbols('lambda[0] lambda[1] lambda[2] lambda[3] eta') lf0, lf1 = symbols('lambda_f[0] lambda_f[1]') # declare variables a = dendro.scalar("alpha", "[pp]") chi = dendro.scalar("chi", "[pp]") K = dendro.scalar("K", "[pp]") Gt = dendro.vec3("Gt", "[pp]") b = dendro.vec3("beta", "[pp]") B = dendro.vec3("B", "[pp]") gt = dendro.sym_3x3("gt", "[pp]") At = dendro.sym_3x3("At", "[pp]") # note: these are just the symbolic vars that is being used to generate the # Gt_rhs by satges _Gt_rhs_s1 = dendro.vec3("Gt_rhs_s1_", "[pp]") _Gt_rhs_s2 = dendro.vec3("Gt_rhs_s2_", "[pp]") _Gt_rhs_s3 = dendro.vec3("Gt_rhs_s3_", "[pp]") _Gt_rhs_s4 = dendro.vec3("Gt_rhs_s4_", "[pp]") _Gt_rhs_s5 = dendro.vec3("Gt_rhs_s5_", "[pp]") _Gt_rhs_s6 = dendro.vec3("Gt_rhs_s6_", "[pp]")
import dendro from sympy import * ################################################################### # initialize ################################################################### l1, l2, l3, l4, eta = symbols('lambda[0] lambda[1] lambda[2] lambda[3] eta') lf0, lf1 = symbols('lambda_f[0] lambda_f[1]') # declare variables a = dendro.scalar("alpha") chi = dendro.scalar("chi") K = dendro.scalar("K") Gt = dendro.vec3("Gt") b = dendro.vec3("beta") B = dendro.vec3("B") gt = dendro.sym_3x3("gt") At = dendro.sym_3x3("At") Gt_rhs = dendro.vec3("Gt_rhs") # Lie derivative weight weight = -2 / 3 weight_Gt = 2 / 3 # specify the functions for computing first and second derivatives d = dendro.set_first_derivative('grad') # first argument is direction d2 = dendro.set_second_derivative('grad2') # first 2 arguments are directions
#!/usr/bin/env/ python3 import dendro from sympy import * ################################################################### # initialize ################################################################### # Declare variables. # These include the BSSN variables that we need for the Psi4 # calculation. chi = dendro.scalar("chi", "[pp]") K = dendro.scalar("K", "[pp]") Gt = dendro.vec3("Gt", "[pp]") gt = dendro.sym_3x3("gt", "[pp]") At = dendro.sym_3x3("At", "[pp]") # Define some symbolic variables that will be used to stage the # calculation of the constraints. _ham_s1 = dendro.scalar("ham_s1_", "[pp]") _ham_s2 = dendro.scalar("ham_s2_", "[pp]") _mom_s1 = dendro.vec3("mom_s1_", "[pp]") _mom_s2 = dendro.vec3("mom_s2_", "[pp]") _mom_s3 = dendro.vec3("mom_s3_", "[pp]") # Now for the same variables that will be used to generate the code ham_s1 = dendro.scalar("ham_s1_", "[pp]") ham_s2 = dendro.scalar("ham_s2_", "[pp]") mom_s1 = dendro.scalar("mom_s1_", "[pp]")
#!/usr/bin/env/ python3 import dendro from sympy import * ################################################################### # initialize ################################################################### # Declare variables. # These include the BSSN variables that we need for the Psi4 # calculation. chi = dendro.scalar("chi", "[pp]") K = dendro.scalar("K", "[pp]") Gt = dendro.vec3("Gt", "[pp]") gt = dendro.sym_3x3("gt", "[pp]") At = dendro.sym_3x3("At", "[pp]") b = dendro.vec3("beta", "[pp]") a = dendro.scalar("alpha", "[pp]") # declare reference metric related vars # TODO : this is not really evolution variables... but somewhat need to be defined #a_ref = dendro.scalar("alpha_ref", "[pp]") #b_ref = dendro.vec3("beta_ref", "[pp]") #f_ref = dendro.sym_3x3("f_ref", "[pp]") # Alternative way (same as in evolution eqs part) a_ref = 1 b_ref = Matrix([[0, 0, 0]]) f_ref = eye(3)
############################################################################### import dendro from sympy import * from sympy.physics.vector.vector import Vector from sympy.printing.dot import dotprint ################################################################### # initialize ################################################################### l1, l2, l3, l4, eta = symbols('lambda[0] lambda[1] lambda[2] lambda[3] eta') lf0, lf1 = symbols('lambda_f[0] lambda_f[1]') # declare variables RccSc = dendro.scalar("RccSc", "[pp]") Vaux = dendro.vec3("Vaux", "[pp]") gm = dendro.sym_3x3("gm", "[pp]") Rcct = dendro.sym_3x3("Rcct", "[pp]") # Lie derivative weight weight = -Rational(2,3) weight_Gt = Rational(2,3) # specify the functions for computing first and second derivatives d = dendro.set_first_derivative('grad') # first argument is direction d2s = dendro.set_second_derivative('grad2') # first 2 arguments are directions ad = dendro.set_advective_derivative('agrad') # first argument is direction kod = dendro.set_kreiss_oliger_dissipation('kograd') d2 = dendro.d2