def METHOD_NAME(self, dirichletvalues):
    a, u, w, r = self.a, self.u, self.w, self.r
    a.AssembleLinearization(u.vec)
    self._UpdateInverse()
    w.data = dirichletvalues-u.vec
    r.data = a.mat * w
    w.data -= self.inv*r
    u.vec.data += w