# Problem with triple NIntegrate

I am a new to Mathematica. I want to calculate a triple integral but Mathematica returned SystemException["MemoryAllocationFailure"].

ClearAll["Global*"]
Ri = 10.5/10^3;
Ro = 11.5/10^3;
h = 1/10^3;
c = 30/10^3;
l = 3/10^3;
μ = (4*Pi)/10^7;
i0 = 1;
f = 0.159*10^9;
ω = 2*Pi*f;
σ = 1;
Subscript[Λ, 2] = Sqrt[γ^2 + I*ω*μ*σ];
ℒ = ((μ*Pi)/(h*(Ri - Ro))^2)*NIntegrate[(r*BesselJ[1, γ*r])*
(R0*BesselJ[1, γ*R0])*((1 - E^((-h)*γ))^2/(E^(2*l*γ)*γ^2))*
((E^(2*c*γ + 2*(c + 2*h + l)*Subscript[Λ, 2])*
(-1 + E^(2*c*Subscript[Λ, 2]))*(γ - Subscript[Λ, 2])*
(γ + Subscript[Λ, 2])*
((-(E^(2*(2*h + l)*γ) + E^(2*c*Subscript[Λ, 2])))*
(γ - Subscript[Λ, 2])^2 +
(1 + E^(4*h*γ + 2*l*γ + 2*c*Subscript[Λ, 2]))*(γ + Subscript[Λ, 2])^
2))/(E^(2*(c + 2*h + l)*(γ + Subscript[Λ, 2]))*
(γ - Subscript[Λ, 2])^4 +
E^(2*(c + 2*h + l)*γ + 2*(3*c + 2*h + l)*Subscript[Λ, 2])*
(γ + Subscript[Λ, 2])^4 - E^(2*c*γ + 2*(c + 2*h + l)*Subscript[Λ, 2])*
(2*E^(4*h*γ + 2*l*γ + 2*c*Subscript[Λ, 2]) +
(-1 + E^(2*c*Subscript[Λ, 2]))^2)*(γ^2 - Subscript[Λ, 2]^2)^2)),
{γ, 0, Infinity}, {r, Ri, Ro}, {R0, Ri, Ro}]


I changed some of the option values -- is this a result you expect:

Ri = 10.5/10^3;
Ro = 11.5/10^3;
h = 1/10^3;
c = 30/10^3;
l = 3/10^3;
\[Mu] = (4*Pi)/10^7;
i0 = 1;
f = 0.159*10^9;
\[Omega] = 2*Pi*f;
\[Sigma] = 1;

L2 = Sqrt[\[Gamma]^2 + I*\[Omega]*\[Mu]*\[Sigma]];

\[ScriptCapitalL] = ((\[Mu]*Pi)/(h*(Ri - Ro))^2)*
NIntegrate[(r*BesselJ[1, \[Gamma]*r])*(R0*
BesselJ[1, \[Gamma]*
R0])*((1 -
E^((-h)*\[Gamma]))^2/(E^(2*
l*\[Gamma])*\[Gamma]^2))*((E^(2*c*\[Gamma] +
2*(c + 2*h + l)*L2)*(-1 + E^(2*c*L2))*(\[Gamma] -
L2)*(\[Gamma] +
L2)*((-(E^(2*(2*h + l)*\[Gamma]) + E^(2*c*L2)))*(\[Gamma] -
L2)^2 + (1 +
E^(4*h*\[Gamma] + 2*l*\[Gamma] + 2*c*L2))*(\[Gamma] +
L2)^2))/(E^(2*(c + 2*h + l)*(\[Gamma] + L2))*(\[Gamma] -
L2)^4 +
E^(2*(c + 2*h + l)*\[Gamma] +
2*(3*c + 2*h + l)*L2)*(\[Gamma] + L2)^4 -
E^(2*c*\[Gamma] + 2*(c + 2*h + l)*L2)*(2*
E^(4*h*\[Gamma] + 2*l*\[Gamma] + 2*c*L2) + (-1 +
E^(2*c*L2))^2)*(\[Gamma]^2 - L2^2)^2)), {\[Gamma], 0,
Infinity}, {r, Ri, Ro}, {R0, Ri, Ro}, PrecisionGoal -> 3,
Method -> {"LocalAdaptive", "SymbolicProcessing" -> 0}]

(* -6.75294*10^-11 - 2.90231*10^-10 I *)
`
• Thank you sir, I don't know yet but at least it works. I tried to test it with Matlab but Matlab returned me singularity.
– Shan
Commented Aug 17, 2017 at 19:32
• @Shan Ok, good luck with your work! Commented Aug 17, 2017 at 23:06