def GetGradient(self, k):
Jacobian = Add(1.0, self.M.SpMat(), self.dt, self.S.SpMat())
self.Jacobian = Jacobian
add_vector(self.v, self.dt, k, self.w)
add_vector(self.x, self.dt, self.w, self.z)
grad_H = self.H.GetGradientMatrix(self.z)
Jacobian.Add(self.dt**2, grad_H)
return Jacobian
def ImplicitSolve(self, dt, vx, dvx_dt):
sc = self.Height() / 2
v = mfem.Vector(vx, 0, sc)
x = mfem.Vector(vx, sc, sc)
dv_dt = mfem.Vector(dvx_dt, 0, sc)
dx_dt = mfem.Vector(dvx_dt, sc, sc)
# By eliminating kx from the coupled system:
# kv = -M^{-1}*[H(x + dt*kx) + S*(v + dt*kv)]
# kx = v + dt*kv
# we reduce it to a nonlinear equation for kv, represented by the
# backward_euler_oper. This equation is solved with the newton_solver
# object (using J_solver and J_prec internally).
self.backward_euler_oper.SetParameters(dt, v, x)
zero = mfem.Vector() # empty vector is interpreted as
# zero r.h.s. by NewtonSolver
self.newton_solver.Mult(zero, dv_dt)
add_vector(v, dt, dv_dt, dx_dt)
def Mult(self, k, y):
add_vector(self.v, self.dt, k, self.w)
add_vector(self.x, self.dt, self.w, self.z)
self.H.Mult(self.z, y)
self.M.AddMult(k, y)
self.S.AddMult(self.w, y)