ValueError: matmul: Input operand 1 has a mismatch in its core dimension 0,

Question

I am new to python and programming for that matter. I am trying to solve a special type of wave equation using finite element method and carry out simulations in python. I am getting some errors which I do not understand and I need help. Below is the error and subsequently a part of the code.

---

ValueError                                Traceback (most recent call last)
<ipython-input-138-b33b0055e38e> in <module>
      6     # Finite Element Method
      7     #unew = (dt**2) * Minv @ (f*src[it]  -  K @ u) + 2*u - uold
----> 8     vnew = dt * Minv @ (f*src[it]  -  (Kv @ v) -  (Ku @ u)) + v
      9     v = v, vnew
     10     unew = (dt) * vnew

ValueError: matmul: Input operand 1 has a mismatch in its core dimension 0, with gufunc signature (n?,k),(k,m?)->(n?,m?) (size 2 is different from 1000)

Time extrapolation

for it in range(nt):
    # --------------------------------------
    # Finite Element Method
    #unew = (dt**2) * Minv @ (f*src[it]  -  K @ u) + 2*u - uold 
    vnew = dt * Minv @ (f*src[it]  -  (Kv @ v) -  (Ku @ u)) + v 
    v = v, vnew
    unew = (dt) * vnew
    #uold, u = u, unew
    u = u, unew


# --------------------------------------
# Finite Difference Method
pnew = (dt**2) * Mfd @ ( f/dx*src[it]+ D @ p) + 2*p #- pold
p = p, pnew

# --------------------------------------   
# Animation plot. Display both solutions
if not it % iplot:
    for l in line1:
        l.remove()
        del l
    for l in line2:
        l.remove()
        del l
    line1 = plt.plot(x, v, 'k', lw=1.5, label='FEM')
    line2 = plt.plot(x, p, 'r', lw=1.5, label='FDM')
    plt.legend()
    plt.gcf().canvas.draw()

Answer 1

It has to do with your coding style. Your code is too similar to mathematical notion. Issues include doing too much on single line and operator precedence in Python

Your code:

vnew = dt * Minv @ (f*src[it]  -  (Kv @ v) -  (Ku @ u)) + v 

Breaking into simpler statements would allow for easier debugging.

term_1 = (f*src[it])  -  (Kv @ v) -  (Ku @ u)
term_2 = term_1 + v
term_3 =  Minv @ term_2
vnew = dt * term_3