Coverage for pySDC/projects/parallelSDC_reloaded/jacobiElliptic_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 the JacobianElliptic problem 

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 

18# Problem parameters 

19tEnd = 10 

20pName = "JACELL" 

21 

22 

23def getError(uNum, uRef): 

24 if uNum is None: # pragma: no cover 

25 return np.inf 

26 return np.linalg.norm(uRef[-1] - uNum[-1], 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 'ESDIRK53', 

43 'ESDIRK43', 

44 'PIC', 

45 # 'IE', 'LU', 'IEpar', 'PIC', 

46 'MIN-SR-NS', 

47 'MIN-SR-S', 

48 'MIN-SR-FLEX', 

49 # "MIN3", 

50] 

51nStepsList = np.array([10, 20, 50, 100, 200]) 

52# nSweepList = [1, 2, 3, 4] 

53 

54# qDeltaList = ['RK4', 'ESDIRK43', 'MIN-SR-S'] 

55nSweepList = [4] 

56 

57 

58symList = ['o', '^', 's', '>', '*', '<', 'p', '>'] * 10 

59fig, axs = plt.subplots(1, 2) 

60 

61dtVals = tEnd / nStepsList 

62 

63i = 0 

64for qDelta in qDeltaList: 

65 for nSweeps in nSweepList: 

66 sym = symList[i] 

67 i += 1 

68 

69 name = f"{qDelta}({nSweeps})" 

70 try: 

71 params = getParamsRK(qDelta) 

72 name = name[:-3] 

73 if nSweeps != nSweepList[0]: # pragma: no cover 

74 continue 

75 except KeyError: 

76 params = getParamsSDC( 

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

78 ) 

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

80 

81 errors = [] 

82 costs = [] 

83 

84 for nSteps in nStepsList: 

85 print(f' -- nSteps={nSteps} ...') 

86 

87 uRef = solutionExact(tEnd, nSteps, pName) 

88 

89 uSDC, counters, parallel = solutionSDC(tEnd, nSteps, params, pName) 

90 

91 err = getError(uSDC, uRef) 

92 errors.append(err) 

93 

94 cost = getCost(counters) 

95 if parallel: 

96 cost /= nNodes * parEfficiency 

97 costs.append(cost) 

98 

99 # error VS dt 

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

101 # error VS cost 

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

103 

104for i in range(2): 

105 axs[i].set( 

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

107 ylabel=r"$L_\infty$ error", 

108 # ylim=(1e-9, 1e0), 

109 ) 

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

111 axs[i].grid() 

112 

113fig.set_size_inches(12, 5) 

114fig.tight_layout()