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""" 

14import numpy as np 

15import matplotlib.pyplot as plt 

16 

17from pySDC.projects.parallelSDC_reloaded.utils import getParamsSDC, getParamsRK, solutionSDC, solutionExact 

18 

19muVals = [0.1, 2, 10] 

20tEndVals = [6.3, 7.6, 18.9] # tEnd = 1 period for each mu 

21 

22 

23def getError(uNum, uRef): 

24 if uNum is None: 

25 return np.inf 

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

27 

28 

29def getCost(counters): 

30 nNewton, nRHS, tComp = counters 

31 return nNewton + nRHS 

32 

33 

34# Base variable parameters 

35nNodes = 4 

36quadType = 'RADAU-RIGHT' 

37nodeType = 'LEGENDRE' 

38parEfficiency = 1 / nNodes 

39 

40qDeltaList = [ 

41 'RK4', 

42 'ESDIRK43', 

43 'LU', 

44 # 'IE', 'LU', 'IEpar', 'PIC', 

45 'MIN-SR-NS', 

46 'MIN-SR-S', 

47 'MIN-SR-FLEX', 

48] 

49nStepsList = np.array([2, 5, 10, 20, 50, 100, 200]) 

50nSweepList = [1, 2, 3, 4, 5, 6] 

51 

52 

53symList = ['o', '^', 's', '>', '*', '<', 'p', '>'] * 10 

54 

55# qDeltaList = ['LU'] 

56nSweepList = [4] 

57 

58fig, axs = plt.subplots(2, len(muVals)) 

59 

60for j, (mu, tEnd) in enumerate(zip(muVals, tEndVals)): 

61 print("-" * 80) 

62 print(f"mu={mu}") 

63 print("-" * 80) 

64 

65 dtVals = tEnd / nStepsList 

66 

67 i = 0 

68 for qDelta in qDeltaList: 

69 for nSweeps in nSweepList: 

70 sym = symList[i] 

71 i += 1 

72 

73 name = f"{qDelta}({nSweeps})" 

74 try: 

75 params = getParamsRK(qDelta) 

76 name = name[:-3] 

77 except KeyError: 

78 params = getParamsSDC( 

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

80 ) 

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

82 

83 errors = [] 

84 costs = [] 

85 

86 for nSteps in nStepsList: 

87 print(f' -- nSteps={nSteps} ...') 

88 

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

90 

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

92 

93 err = getError(uSDC, uRef) 

94 errors.append(err) 

95 

96 cost = getCost(counters) 

97 if parallel: 

98 cost /= nNodes * parEfficiency 

99 costs.append(cost) 

100 

101 # error VS dt 

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

103 # error VS cost 

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

105 

106 for i in range(2): 

107 if i == 0: 

108 axs[i, j].set_title(f"mu={mu}") 

109 axs[i, j].set( 

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

111 ylabel=r"$L_\infty$ error", 

112 ylim=(1e-11, 10), 

113 ) 

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

115 axs[i, j].grid() 

116 

117fig.set_size_inches(18.2, 10.4) 

118fig.tight_layout()