Coverage for pySDC / projects / parallelSDC_reloaded / vanderpol_accuracy.py: 100%

1#!/usr/bin/env python3 

2# -*- coding: utf-8 -*- 

3""" 

4Created on Sun Nov 12 22:14:03 2023 

5 

6Script to investigate diagonal SDC on Van der Pol with different mu parameters, 

7in particular with graphs such as : 

8 

9- error VS time-step 

10- error VS computation cost 

11 

12Note : implementation in progress ... 

13""" 

14 

15import numpy as np 

16import matplotlib.pyplot as plt 

17 

18from pySDC.projects.parallelSDC_reloaded.utils import getParamsSDC, getParamsRK, solutionSDC, solutionExact 

19 

20muVals = [0.1, 2, 10] 

21tEndVals = [6.3, 7.6, 18.9] # tEnd = 1 period for each mu 

22 

23 

24def getError(uNum, uRef): 

25 if uNum is None: 

26 return np.inf 

27 return np.linalg.norm(uRef[:, 0] - uNum[:, 0], np.inf) 

28 

29 

30def getCost(counters): 

31 nNewton, nRHS, tComp = counters 

32 return nNewton + nRHS 

33 

34 

35# Base variable parameters 

36nNodes = 4 

37quadType = 'RADAU-RIGHT' 

38nodeType = 'LEGENDRE' 

39parEfficiency = 1 / nNodes 

40 

41qDeltaList = [ 

42 'RK4', 

43 'ESDIRK43', 

44 'LU', 

45 # 'IE', 'LU', 'IEpar', 'PIC', 

46 'MIN-SR-NS', 

47 'MIN-SR-S', 

48 'MIN-SR-FLEX', 

49] 

50nStepsList = np.array([2, 5, 10, 20, 50, 100, 200]) 

51nSweepList = [1, 2, 3, 4, 5, 6] 

52 

53 

54symList = ['o', '^', 's', '>', '*', '<', 'p', '>'] * 10 

55 

56# qDeltaList = ['LU'] 

57nSweepList = [4] 

58 

59fig, axs = plt.subplots(2, len(muVals)) 

60 

61for j, (mu, tEnd) in enumerate(zip(muVals, tEndVals, strict=True)): 

62 print("-" * 80) 

63 print(f"mu={mu}") 

64 print("-" * 80) 

65 

66 dtVals = tEnd / nStepsList 

67 

68 i = 0 

69 for qDelta in qDeltaList: 

70 for nSweeps in nSweepList: 

71 sym = symList[i] 

72 i += 1 

73 

74 name = f"{qDelta}({nSweeps})" 

75 try: 

76 params = getParamsRK(qDelta) 

77 name = name[:-3] 

78 except KeyError: 

79 params = getParamsSDC( 

80 quadType=quadType, numNodes=nNodes, nodeType=nodeType, qDeltaI=qDelta, nSweeps=nSweeps 

81 ) 

82 print(f'computing for {name} ...') 

83 

84 errors = [] 

85 costs = [] 

86 

87 for nSteps in nStepsList: 

88 print(f' -- nSteps={nSteps} ...') 

89 

90 uRef = solutionExact(tEnd, nSteps, "VANDERPOL", mu=mu) 

91 

92 uSDC, counters, parallel = solutionSDC(tEnd, nSteps, params, "VANDERPOL", mu=mu) 

93 

94 err = getError(uSDC, uRef) 

95 errors.append(err) 

96 

97 cost = getCost(counters) 

98 if parallel: 

99 cost /= nNodes * parEfficiency 

100 costs.append(cost) 

101 

102 # error VS dt 

103 axs[0, j].loglog(dtVals, errors, sym + '-', label=name) 

104 # error VS cost 

105 axs[1, j].loglog(costs, errors, sym + '-', label=name) 

106 

107 for i in range(2): 

108 if i == 0: 

109 axs[i, j].set_title(f"mu={mu}") 

110 axs[i, j].set( 

111 xlabel=r"$\Delta{t}$" if i == 0 else "cost", 

112 ylabel=r"$L_\infty$ error", 

113 ylim=(1e-11, 10), 

114 ) 

115 axs[i, j].legend(loc="lower right" if i == 0 else "lower left") 

116 axs[i, j].grid() 

117 

118fig.set_size_inches(18.2, 10.4) 

119fig.tight_layout()