Maybe in your case the NIntegrate
or NMinimize
aborted internally due to the poor convergence with the default method.Good news is that I notice your functions are rather smooth and the target function is semi-quadratic. So you can use some built-in method to boost up computation speed
intI[m_ ...] := 1/(2 Pi)*Chop@NIntegrate[... , AccuracyGoal -> 5, Method -> "TrapezoidalRule"];
intJ[m_ ...]:= 1/(2 Pi)*Chop@NIntegrate[... , AccuracyGoal -> 5, Method -> "TrapezoidalRule"];
Use NMinimize or FindMinimum with specified methods:
Minima = ParallelTable[
NMinimize[{HeffSinAns[1.2, 1.2, L, ValuesMN[[j, 1]],
ValuesMN[[j, 2]], ph0, th0, th1, K1, K2], -\[Pi] <=
th0 < \[Pi], -\[Pi] <= ph0 < \[Pi], -\[Pi] <= th1 < \[Pi]}, {L,
ph0, th0, th1, K1, K2},
Method -> {"SimulatedAnnealing",
"PerturbationScale" -> 3}, MaxIterations -> 10], {j, 1, Length[ValuesMN]}]
I found this give you good approximations within 130 seconds for all cases on a 6-core i7 laptop