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

1#!/usr/bin/env python3 

2# -*- coding: utf-8 -*- 

3""" 

4Created on Tue Dec 5 11:02:39 2023 

5 

6Script to investigate diagonal SDC on Lorenz system 

7 

8- error VS time-step 

9- error VS computation cost 

10 

11Note : implementation in progress ... 

12""" 

13import numpy as np 

14import matplotlib.pyplot as plt 

15 

16from pySDC.projects.parallelSDC_reloaded.utils import getParamsSDC, getParamsRK, solutionSDC, solutionExact 

17 

18tEnd = 1.24 

19 

20 

21def getError(uNum, uRef): 

22 if uNum is None: # pragma: no cover 

23 return np.inf 

24 return np.linalg.norm(np.linalg.norm(uRef - uNum, np.inf, axis=-1), np.inf) 

25 

26 

27def getCost(counters): 

28 nNewton, nRHS, tComp = counters 

29 return nNewton + nRHS 

30 

31 

32# Base variable parameters 

33nNodes = 4 

34quadType = 'RADAU-RIGHT' 

35nodeType = 'LEGENDRE' 

36parEfficiency = 0.8 # 1/nNodes 

37 

38qDeltaList = [ 

39 'RK4', 

40 'ESDIRK53', 

41 'VDHS', 

42 'MIN', 

43 # 'IE', 'LU', 'IEpar', 'PIC', 

44 'MIN-SR-NS', 

45 'MIN-SR-S', 

46 'MIN-SR-FLEX', 

47 "PIC", 

48 # "MIN3", 

49] 

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

51nSweepList = [1, 2, 3, 4] 

52 

53 

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

55 

56qDeltaList = ['MIN-SR-S', 'RK4'] 

57# nSweepList = [4] 

58 

59fig, axs = plt.subplots(1, 2) 

60 

61 

62dtVals = tEnd / nStepsList 

63 

64i = 0 

65for qDelta in qDeltaList: 

66 for nSweeps in nSweepList: 

67 sym = symList[i] 

68 i += 1 

69 

70 name = f"{qDelta}({nSweeps})" 

71 try: 

72 params = getParamsRK(qDelta) 

73 name = name[:-3] 

74 if nSweeps != nSweepList[0]: 

75 continue 

76 except KeyError: 

77 params = getParamsSDC( 

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

79 ) 

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

81 

82 errors = [] 

83 costs = [] 

84 

85 for nSteps in nStepsList: 

86 print(f' -- nSteps={nSteps} ...') 

87 

88 uRef = solutionExact(tEnd, nSteps, "LORENZ", u0=(5, -5, 20)) 

89 

90 uSDC, counters, parallel = solutionSDC(tEnd, nSteps, params, "LORENZ", u0=(5, -5, 20)) 

91 

92 err = getError(uSDC, uRef) 

93 errors.append(err) 

94 

95 cost = getCost(counters) 

96 if parallel: 

97 cost /= nNodes * parEfficiency 

98 costs.append(cost) 

99 

100 # error VS dt 

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

102 # error VS cost 

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

104 

105x = dtVals[4:] 

106for k in [1, 2, 3, 4, 5]: 

107 axs[0].loglog(x, 1e4 * x**k, "--", color="gray", linewidth=0.8) 

108 

109for i in range(2): 

110 axs[i].set( 

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

112 ylabel=r"$L_\infty$ error", 

113 ylim=(8.530627786509715e-12, 372.2781393394293), 

114 ) 

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

116 axs[i].grid() 

117 

118fig.set_size_inches(12, 5) 

119fig.tight_layout()