An Efficient Approach for Solving Mesh Optimization Problems Using Newton’s Method

Algorithm 4

Volume mesh optimization and untangling using Newton’s method.

while  not converged  do

 Compute the gradient and Hessian

 if   is not positive definite  then

   Perform Hessian modification

 end if

 Newton direction:

 Update the vertex position: such that satisfies the  

 if   satisfies mesh validity  then

   Update the vertex position

 else

   Backtracking Line Search: set ,

 end if

end while