Coverage for pySDC / projects / parallelSDC_reloaded / protheroRobinson_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 ProtheroRobinson 

7(linear and non-linear) problem : 

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 

20# Problem parameters 

21tEnd = 2 * np.pi 

22nonLinear = False 

23epsilon = 1e-3 

24collUpdate = False 

25initSweep = "copy" 

26 

27pName = "PROTHERO-ROBINSON" + (nonLinear) * "-NL" 

28 

29 

30def getError(uNum, uRef): 

31 if uNum is None: 

32 return np.inf 

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

34 

35 

36def getCost(counters): 

37 nNewton, nRHS, tComp = counters 

38 return nNewton + nRHS 

39 

40 

41# Base variable parameters 

42nNodes = 4 

43quadType = 'RADAU-RIGHT' 

44nodeType = 'LEGENDRE' 

45parEfficiency = 0.8 

46 

47qDeltaList = [ 

48 'MIN-SR-NS', 

49 'MIN-SR-S', 

50 'MIN-SR-FLEX', 

51 "ESDIRK43", 

52 'LU', 

53 'VDHS', 

54 # 'IE', 'LU', 'IEpar', 'PIC', 

55 # "MIN3", 

56] 

57nStepsList = np.array([2, 5, 10, 20, 50, 100, 200]) 

58# nSweepList = [1, 2, 3, 4] 

59 

60# qDeltaList = ['ESDIRK43', 'ESDIRK53', 'VDHS'] 

61nSweepList = [6] 

62 

63 

64symList = ['o', '^', 's', '>', '*', '<', 'p', '>'] * 10 

65fig, axs = plt.subplots(1, 2) 

66 

67dtVals = tEnd / nStepsList 

68 

69i = 0 

70for qDelta in qDeltaList: 

71 for nSweeps in nSweepList: 

72 sym = symList[i] 

73 i += 1 

74 

75 name = f"{qDelta}({nSweeps})" 

76 try: 

77 params = getParamsRK(qDelta) 

78 name = name.split('(')[0] 

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

80 continue 

81 

82 except KeyError: 

83 params = getParamsSDC( 

84 quadType=quadType, 

85 numNodes=nNodes, 

86 nodeType=nodeType, 

87 qDeltaI=qDelta, 

88 nSweeps=nSweeps, 

89 collUpdate=collUpdate, 

90 initType=initSweep, 

91 ) 

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

93 

94 errors = [] 

95 costs = [] 

96 

97 for nSteps in nStepsList: 

98 print(f' -- nSteps={nSteps} ...') 

99 

100 uRef = solutionExact(tEnd, nSteps, pName, epsilon=epsilon) 

101 

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

103 

104 err = getError(uSDC, uRef) 

105 errors.append(err) 

106 

107 cost = getCost(counters) 

108 if parallel: 

109 cost /= nNodes * parEfficiency 

110 costs.append(cost) 

111 

112 # error VS dt 

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

114 # error VS cost 

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

116 

117for i in range(2): 

118 axs[i].set( 

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

120 ylabel=r"$L_\infty$ error", 

121 ylim=(1e-12, 1e3), 

122 ) 

123 axs[i].legend() 

124 axs[i].grid() 

125 

126fig.set_size_inches(12, 5) 

127fig.tight_layout()