#define PDstandard2nd1(u) (p1o2dx*(-(u)[di*(-1)+dj*(0)+dk*(0)] + (u)[di*(1)+dj*(0)+dk*(0)]))
#define PDstandard2nd2(u) (p1o2dy*(-(u)[di*(0)+dj*(-1)+dk*(0)] + (u)[di*(0)+dj*(1)+dk*(0)]))
#define PDstandard2nd3(u) (p1o2dz*(-(u)[di*(0)+dj*(0)+dk*(-1)] + (u)[di*(0)+dj*(0)+dk*(1)]))
#define PDstandard2nd11(u) (p1odx2*(-2*(u)[di*(0)+dj*(0)+dk*(0)] + (u)[di*(-1)+dj*(0)+dk*(0)] + (u)[di*(1)+dj*(0)+dk*(0)]))
#define PDstandard2nd22(u) (p1ody2*(-2*(u)[di*(0)+dj*(0)+dk*(0)] + (u)[di*(0)+dj*(-1)+dk*(0)] + (u)[di*(0)+dj*(1)+dk*(0)]))
#define PDstandard2nd33(u) (p1odz2*(-2*(u)[di*(0)+dj*(0)+dk*(0)] + (u)[di*(0)+dj*(0)+dk*(-1)] + (u)[di*(0)+dj*(0)+dk*(1)]))
#define PDstandard2nd12(u) (p1o4dxdy*((u)[di*(-1)+dj*(-1)+dk*(0)] - (u)[di*(-1)+dj*(1)+dk*(0)] - (u)[di*(1)+dj*(-1)+dk*(0)] + (u)[di*(1)+dj*(1)+dk*(0)]))
#define PDstandard2nd13(u) (p1o4dxdz*((u)[di*(-1)+dj*(0)+dk*(-1)] - (u)[di*(-1)+dj*(0)+dk*(1)] - (u)[di*(1)+dj*(0)+dk*(-1)] + (u)[di*(1)+dj*(0)+dk*(1)]))
#define PDstandard2nd21(u) (p1o4dxdy*((u)[di*(-1)+dj*(-1)+dk*(0)] - (u)[di*(-1)+dj*(1)+dk*(0)] - (u)[di*(1)+dj*(-1)+dk*(0)] + (u)[di*(1)+dj*(1)+dk*(0)]))
#define PDstandard2nd23(u) (p1o4dydz*((u)[di*(0)+dj*(-1)+dk*(-1)] - (u)[di*(0)+dj*(-1)+dk*(1)] - (u)[di*(0)+dj*(1)+dk*(-1)] + (u)[di*(0)+dj*(1)+dk*(1)]))
#define PDstandard2nd31(u) (p1o4dxdz*((u)[di*(-1)+dj*(0)+dk*(-1)] - (u)[di*(-1)+dj*(0)+dk*(1)] - (u)[di*(1)+dj*(0)+dk*(-1)] + (u)[di*(1)+dj*(0)+dk*(1)]))
#define PDstandard2nd32(u) (p1o4dydz*((u)[di*(0)+dj*(-1)+dk*(-1)] - (u)[di*(0)+dj*(-1)+dk*(1)] - (u)[di*(0)+dj*(1)+dk*(-1)] + (u)[di*(0)+dj*(1)+dk*(1)]))
#define PDstandard4th1(u) (p1o12dx*(-8*(u)[di*(-1)+dj*(0)+dk*(0)] + 8*(u)[di*(1)+dj*(0)+dk*(0)] + (u)[di*(-2)+dj*(0)+dk*(0)] - (u)[di*(2)+dj*(0)+dk*(0)]))
#define PDstandard4th2(u) (p1o12dy*(-8*(u)[di*(0)+dj*(-1)+dk*(0)] + 8*(u)[di*(0)+dj*(1)+dk*(0)] + (u)[di*(0)+dj*(-2)+dk*(0)] - (u)[di*(0)+dj*(2)+dk*(0)]))
#define PDstandard4th3(u) (p1o12dz*(-8*(u)[di*(0)+dj*(0)+dk*(-1)] + 8*(u)[di*(0)+dj*(0)+dk*(1)] + (u)[di*(0)+dj*(0)+dk*(-2)] - (u)[di*(0)+dj*(0)+dk*(2)]))
#define PDstandard4th11(u) (pm1o12dx2*(30*(u)[di*(0)+dj*(0)+dk*(0)] - 16*((u)[di*(-1)+dj*(0)+dk*(0)] + (u)[di*(1)+dj*(0)+dk*(0)]) + (u)[di*(-2)+dj*(0)+dk*(0)] + (u)[di*(2)+dj*(0)+dk*(0)]))
#define PDstandard4th22(u) (pm1o12dy2*(30*(u)[di*(0)+dj*(0)+dk*(0)] - 16*((u)[di*(0)+dj*(-1)+dk*(0)] + (u)[di*(0)+dj*(1)+dk*(0)]) + (u)[di*(0)+dj*(-2)+dk*(0)] + (u)[di*(0)+dj*(2)+dk*(0)]))
#define PDstandard4th33(u) (pm1o12dz2*(30*(u)[di*(0)+dj*(0)+dk*(0)] - 16*((u)[di*(0)+dj*(0)+dk*(-1)] + (u)[di*(0)+dj*(0)+dk*(1)]) + (u)[di*(0)+dj*(0)+dk*(-2)] + (u)[di*(0)+dj*(0)+dk*(2)]))
#define PDstandard4th12(u) (p1o144dxdy*(-64*((u)[di*(-1)+dj*(1)+dk*(0)] + (u)[di*(1)+dj*(-1)+dk*(0)]) + 64*((u)[di*(-1)+dj*(-1)+dk*(0)] + (u)[di*(1)+dj*(1)+dk*(0)]) + 8*((u)[di*(-1)+dj*(2)+dk*(0)] + (u)[di*(1)+dj*(-2)+dk*(0)] + (u)[di*(-2)+dj*(1)+dk*(0)] + (u)[di*(2)+dj*(-1)+dk*(0)]) - 8*((u)[di*(-1)+dj*(-2)+dk*(0)] + (u)[di*(1)+dj*(2)+dk*(0)] + (u)[di*(-2)+dj*(-1)+dk*(0)] + (u)[di*(2)+dj*(1)+dk*(0)]) + (u)[di*(-2)+dj*(-2)+dk*(0)] - (u)[di*(-2)+dj*(2)+dk*(0)] - (u)[di*(2)+dj*(-2)+dk*(0)] + (u)[di*(2)+dj*(2)+dk*(0)]))
#define PDstandard4th13(u) (p1o144dxdz*(-64*((u)[di*(-1)+dj*(0)+dk*(1)] + (u)[di*(1)+dj*(0)+dk*(-1)]) + 64*((u)[di*(-1)+dj*(0)+dk*(-1)] + (u)[di*(1)+dj*(0)+dk*(1)]) + 8*((u)[di*(-1)+dj*(0)+dk*(2)] + (u)[di*(1)+dj*(0)+dk*(-2)] + (u)[di*(-2)+dj*(0)+dk*(1)] + (u)[di*(2)+dj*(0)+dk*(-1)]) - 8*((u)[di*(-1)+dj*(0)+dk*(-2)] + (u)[di*(1)+dj*(0)+dk*(2)] + (u)[di*(-2)+dj*(0)+dk*(-1)] + (u)[di*(2)+dj*(0)+dk*(1)]) + (u)[di*(-2)+dj*(0)+dk*(-2)] - (u)[di*(-2)+dj*(0)+dk*(2)] - (u)[di*(2)+dj*(0)+dk*(-2)] + (u)[di*(2)+dj*(0)+dk*(2)]))
#define PDstandard4th21(u) (p1o144dxdy*(-64*((u)[di*(-1)+dj*(1)+dk*(0)] + (u)[di*(1)+dj*(-1)+dk*(0)]) + 64*((u)[di*(-1)+dj*(-1)+dk*(0)] + (u)[di*(1)+dj*(1)+dk*(0)]) + 8*((u)[di*(-1)+dj*(2)+dk*(0)] + (u)[di*(1)+dj*(-2)+dk*(0)] + (u)[di*(-2)+dj*(1)+dk*(0)] + (u)[di*(2)+dj*(-1)+dk*(0)]) - 8*((u)[di*(-1)+dj*(-2)+dk*(0)] + (u)[di*(1)+dj*(2)+dk*(0)] + (u)[di*(-2)+dj*(-1)+dk*(0)] + (u)[di*(2)+dj*(1)+dk*(0)]) + (u)[di*(-2)+dj*(-2)+dk*(0)] - (u)[di*(-2)+dj*(2)+dk*(0)] - (u)[di*(2)+dj*(-2)+dk*(0)] + (u)[di*(2)+dj*(2)+dk*(0)]))
#define PDstandard4th23(u) (p1o144dydz*(-64*((u)[di*(0)+dj*(-1)+dk*(1)] + (u)[di*(0)+dj*(1)+dk*(-1)]) + 64*((u)[di*(0)+dj*(-1)+dk*(-1)] + (u)[di*(0)+dj*(1)+dk*(1)]) + 8*((u)[di*(0)+dj*(-1)+dk*(2)] + (u)[di*(0)+dj*(1)+dk*(-2)] + (u)[di*(0)+dj*(-2)+dk*(1)] + (u)[di*(0)+dj*(2)+dk*(-1)]) - 8*((u)[di*(0)+dj*(-1)+dk*(-2)] + (u)[di*(0)+dj*(1)+dk*(2)] + (u)[di*(0)+dj*(-2)+dk*(-1)] + (u)[di*(0)+dj*(2)+dk*(1)]) + (u)[di*(0)+dj*(-2)+dk*(-2)] - (u)[di*(0)+dj*(-2)+dk*(2)] - (u)[di*(0)+dj*(2)+dk*(-2)] + (u)[di*(0)+dj*(2)+dk*(2)]))
#define PDstandard4th31(u) (p1o144dxdz*(-64*((u)[di*(-1)+dj*(0)+dk*(1)] + (u)[di*(1)+dj*(0)+dk*(-1)]) + 64*((u)[di*(-1)+dj*(0)+dk*(-1)] + (u)[di*(1)+dj*(0)+dk*(1)]) + 8*((u)[di*(-1)+dj*(0)+dk*(2)] + (u)[di*(1)+dj*(0)+dk*(-2)] + (u)[di*(-2)+dj*(0)+dk*(1)] + (u)[di*(2)+dj*(0)+dk*(-1)]) - 8*((u)[di*(-1)+dj*(0)+dk*(-2)] + (u)[di*(1)+dj*(0)+dk*(2)] + (u)[di*(-2)+dj*(0)+dk*(-1)] + (u)[di*(2)+dj*(0)+dk*(1)]) + (u)[di*(-2)+dj*(0)+dk*(-2)] - (u)[di*(-2)+dj*(0)+dk*(2)] - (u)[di*(2)+dj*(0)+dk*(-2)] + (u)[di*(2)+dj*(0)+dk*(2)]))
#define PDstandard4th32(u) (p1o144dydz*(-64*((u)[di*(0)+dj*(-1)+dk*(1)] + (u)[di*(0)+dj*(1)+dk*(-1)]) + 64*((u)[di*(0)+dj*(-1)+dk*(-1)] + (u)[di*(0)+dj*(1)+dk*(1)]) + 8*((u)[di*(0)+dj*(-1)+dk*(2)] + (u)[di*(0)+dj*(1)+dk*(-2)] + (u)[di*(0)+dj*(-2)+dk*(1)] + (u)[di*(0)+dj*(2)+dk*(-1)]) - 8*((u)[di*(0)+dj*(-1)+dk*(-2)] + (u)[di*(0)+dj*(1)+dk*(2)] + (u)[di*(0)+dj*(-2)+dk*(-1)] + (u)[di*(0)+dj*(2)+dk*(1)]) + (u)[di*(0)+dj*(-2)+dk*(-2)] - (u)[di*(0)+dj*(-2)+dk*(2)] - (u)[di*(0)+dj*(2)+dk*(-2)] + (u)[di*(0)+dj*(2)+dk*(2)]))
#define PDplus1(u) (p1odx*(-(u)[di*(0)+dj*(0)+dk*(0)] + (u)[di*(1)+dj*(0)+dk*(0)]))
#define PDplus2(u) (p1ody*(-(u)[di*(0)+dj*(0)+dk*(0)] + (u)[di*(0)+dj*(1)+dk*(0)]))
#define PDplus3(u) (p1odz*(-(u)[di*(0)+dj*(0)+dk*(0)] + (u)[di*(0)+dj*(0)+dk*(1)]))
#define PDminus1(u) (p1odx*((u)[di*(0)+dj*(0)+dk*(0)] - (u)[di*(-1)+dj*(0)+dk*(0)]))
#define PDminus2(u) (p1ody*((u)[di*(0)+dj*(0)+dk*(0)] - (u)[di*(0)+dj*(-1)+dk*(0)]))
#define PDminus3(u) (p1odz*((u)[di*(0)+dj*(0)+dk*(0)] - (u)[di*(0)+dj*(0)+dk*(-1)]))
#define PDplus11(u) (p1odx2*((u)[di*(0)+dj*(0)+dk*(0)] - 2*(u)[di*(1)+dj*(0)+dk*(0)] + (u)[di*(2)+dj*(0)+dk*(0)]))
#define PDplus12(u) (p1odxdy*((u)[di*(0)+dj*(0)+dk*(0)] - (u)[di*(0)+dj*(1)+dk*(0)] - (u)[di*(1)+dj*(0)+dk*(0)] + (u)[di*(1)+dj*(1)+dk*(0)]))
#define PDplus13(u) (p1odxdz*((u)[di*(0)+dj*(0)+dk*(0)] - (u)[di*(0)+dj*(0)+dk*(1)] - (u)[di*(1)+dj*(0)+dk*(0)] + (u)[di*(1)+dj*(0)+dk*(1)]))
#define PDplus21(u) (p1odxdy*((u)[di*(0)+dj*(0)+dk*(0)] - (u)[di*(0)+dj*(1)+dk*(0)] - (u)[di*(1)+dj*(0)+dk*(0)] + (u)[di*(1)+dj*(1)+dk*(0)]))
#define PDplus22(u) (p1ody2*((u)[di*(0)+dj*(0)+dk*(0)] - 2*(u)[di*(0)+dj*(1)+dk*(0)] + (u)[di*(0)+dj*(2)+dk*(0)]))
#define PDplus23(u) (p1odydz*((u)[di*(0)+dj*(0)+dk*(0)] - (u)[di*(0)+dj*(0)+dk*(1)] - (u)[di*(0)+dj*(1)+dk*(0)] + (u)[di*(0)+dj*(1)+dk*(1)]))
#define PDplus31(u) (p1odxdz*((u)[di*(0)+dj*(0)+dk*(0)] - (u)[di*(0)+dj*(0)+dk*(1)] - (u)[di*(1)+dj*(0)+dk*(0)] + (u)[di*(1)+dj*(0)+dk*(1)]))
#define PDplus32(u) (p1odydz*((u)[di*(0)+dj*(0)+dk*(0)] - (u)[di*(0)+dj*(0)+dk*(1)] - (u)[di*(0)+dj*(1)+dk*(0)] + (u)[di*(0)+dj*(1)+dk*(1)]))
#define PDplus33(u) (p1odz2*((u)[di*(0)+dj*(0)+dk*(0)] - 2*(u)[di*(0)+dj*(0)+dk*(1)] + (u)[di*(0)+dj*(0)+dk*(2)]))
#define PDonesided2nd1(u) (pm1o2dx*(3*(u)[di*(0)+dj*(0)+dk*(0)] + (u)[di*(2*dir(1))+dj*(0)+dk*(0)] - 4*(u)[di*(dir(1))+dj*(0)+dk*(0)])*dir(1))
#define PDonesided2nd2(u) (pm1o2dy*(3*(u)[di*(0)+dj*(0)+dk*(0)] + (u)[di*(0)+dj*(2*dir(2))+dk*(0)] - 4*(u)[di*(0)+dj*(dir(2))+dk*(0)])*dir(2))
#define PDonesided2nd3(u) (pm1o2dz*(3*(u)[di*(0)+dj*(0)+dk*(0)] + (u)[di*(0)+dj*(0)+dk*(2*dir(3))] - 4*(u)[di*(0)+dj*(0)+dk*(dir(3))])*dir(3))