Coverage for pySDC/implementations/sweeper_classes/generic_implicit.py: 100%

1from pySDC.core.sweeper import Sweeper 

2 

3 

4class generic_implicit(Sweeper): 

5 """ 

6 Generic implicit sweeper, expecting lower triangular matrix type as input 

7 

8 Attributes: 

9 QI: lower triangular matrix 

10 """ 

11 

12 def __init__(self, params, level): 

13 """ 

14 Initialization routine for the custom sweeper 

15 

16 Args: 

17 params: parameters for the sweeper 

18 level (pySDC.Level.level): the level that uses this sweeper 

19 """ 

20 

21 if 'QI' not in params: 

22 params['QI'] = 'IE' 

23 

24 super().__init__(params, level) 

25 

26 # get QI matrix 

27 self.QI = self.get_Qdelta_implicit(qd_type=self.params.QI) 

28 

29 def integrate(self): 

30 """ 

31 Integrates the right-hand side 

32 

33 Returns: 

34 list of dtype_u: containing the integral as values 

35 """ 

36 

37 L = self.level 

38 P = L.prob 

39 

40 me = [] 

41 

42 # integrate RHS over all collocation nodes 

43 for m in range(1, self.coll.num_nodes + 1): 

44 # new instance of dtype_u, initialize values with 0 

45 me.append(P.dtype_u(P.init, val=0.0)) 

46 for j in range(1, self.coll.num_nodes + 1): 

47 me[-1] += L.dt * self.coll.Qmat[m, j] * L.f[j] 

48 

49 return me 

50 

51 def update_nodes(self): 

52 """ 

53 Update the u- and f-values at the collocation nodes -> corresponds to a single sweep over all nodes 

54 

55 Returns: 

56 None 

57 """ 

58 

59 L = self.level 

60 P = L.prob 

61 

62 # only if the level has been touched before 

63 assert L.status.unlocked 

64 

65 # get number of collocation nodes for easier access 

66 M = self.coll.num_nodes 

67 

68 # the terms which are known already (from the previous iteration) are u0 + QF(u^k) - QdF(u^k) + tau, built 

69 # with Q - Qd in one pass over F(u^k), kept here because the sweep replaces L.f[m] 

70 F = L.f[1:] 

71 diff_weights = self.coll.Qmat - self.QI 

72 

73 # do the sweep 

74 for m in range(0, M): 

75 # build rhs, consisting of the known values and new values from previous nodes (at k+1) 

76 rhs = P.dtype_u(L.u[0]) 

77 for j in range(1, M + 1): 

78 rhs += L.dt * diff_weights[m + 1, j] * F[j - 1] 

79 if L.tau[m] is not None: 

80 rhs += L.tau[m] 

81 for j in range(1, m + 1): 

82 rhs += L.dt * self.QI[m + 1, j] * L.f[j] 

83 

84 # implicit solve with prefactor stemming from the diagonal of Qd 

85 alpha = L.dt * self.QI[m + 1, m + 1] 

86 if alpha == 0: 

87 L.u[m + 1] = rhs 

88 else: 

89 L.u[m + 1] = P.solve_system(rhs, alpha, L.u[m + 1], L.time + L.dt * self.coll.nodes[m]) 

90 # update function values 

91 L.f[m + 1] = P.eval_f(L.u[m + 1], L.time + L.dt * self.coll.nodes[m]) 

92 

93 # indicate presence of new values at this level 

94 L.status.updated = True 

95 

96 return None 

97 

98 def compute_end_point(self): 

99 """ 

100 Compute u at the right point of the interval 

101 

102 The value uend computed here is a full evaluation of the Picard formulation unless do_full_update==False 

103 

104 Returns: 

105 None 

106 """ 

107 

108 L = self.level 

109 P = L.prob 

110 

111 # check if Mth node is equal to right point and do_coll_update is false, perform a simple copy 

112 if self.coll.right_is_node and not self.params.do_coll_update: 

113 # a copy is sufficient 

114 L.uend = P.dtype_u(L.u[-1]) 

115 else: 

116 # start with u0 and add integral over the full interval (using coll.weights) 

117 L.uend = P.dtype_u(L.u[0]) 

118 for m in range(self.coll.num_nodes): 

119 L.uend += L.dt * self.coll.weights[m] * L.f[m + 1] 

120 # add up tau correction of the full interval (last entry) 

121 if L.tau[-1] is not None: 

122 L.uend += L.tau[-1] 

123 

124 return None