Bug introduced in 12.1 or earlier, fixed in 12.2.
In the above code, the InterpolatingFunction object has order -1. In the documentation https://reference.wolfram.com/language/ref/InterpolationOrder.html, it seems that InterpolationOrder has to be $\geq 0$. What is the meaning of the negative InterpolationOrder?
Added:
I am using version 12.1.
I obtained many InterpolatingFunction object after the below NDEigensolve
command.
NDEigensystem[{{3*psi3[x, y] - 10*psi2[x, y]*Sign[y] - Derivative[0, 1][psi2][x, y] -
I*Derivative[1, 0][psi2][x, y], 3*psi4[x, y] - 10*psi1[x, y]*Sign[y] + Derivative[0, 1][psi1][x, y] -
I*Derivative[1, 0][psi1][x, y], 3*psi1[x, y] - 10*psi4[x, y]*Sign[y] - Derivative[0, 1][psi4][x, y] -
I*Derivative[1, 0][psi4][x, y], 3*psi2[x, y] - 10*psi3[x, y]*Sign[y] + Derivative[0, 1][psi3][x, y] -
I*Derivative[1, 0][psi3][x, y]}, PeriodicBoundaryCondition[psi1[x, y], x == 0,
TransformationFunction[{{1, 0, 20}, {0, 1, 0}, {0, 0, 1}}]], PeriodicBoundaryCondition[psi2[x, y], x == 0,
TransformationFunction[{{1, 0, 20}, {0, 1, 0}, {0, 0, 1}}]], PeriodicBoundaryCondition[psi3[x, y], x == 0,
TransformationFunction[{{1, 0, 20}, {0, 1, 0}, {0, 0, 1}}]], PeriodicBoundaryCondition[psi4[x, y], x == 0,
TransformationFunction[{{1, 0, 20}, {0, 1, 0}, {0, 0, 1}}]], DirichletCondition[psi1[x, y] == 0,
0 < x < 20 && (y == 70 || y == -70)], DirichletCondition[psi2[x, y] == 0,
0 < x < 20 && (y == 70 || y == -70)], DirichletCondition[psi3[x, y] == 0,
0 < x < 20 && (y == 70 || y == -70)], DirichletCondition[psi4[x, y] == 0,
0 < x < 20 && (y == 70 || y == -70)]}, {psi1, psi2, psi3, psi4}, Element[{x, y}, Rectangle[{0,-70}, {20,70}]], 10]
In the code, I am trying to obtain the eigenvalue of a certain $4\times 4$ matrix differential operator. The region I consider is a rectangle of size $20\times 140$. At left and right side, I applied the periodic boundary condition. At top and bottom side, I applied the Dirichlet boundary condition. The differential operator is the form
$$h_x \partial_x + h_y \partial_y + h_0(x,y),$$
where $h_x, h_y, h_0(x,y)$ are $4\times 4$ matrices. The dependent variable is denoted as {psi1[x,y], psi2[x,y], psi3[x,y], psi4[x,y]}
.