A Practical Approach for Solving Mesh Optimization Problems using Newton’s Method

We present a practical approach for solving volume and surface mesh optimization problems. Our approach is based on Newton’s method which uses both first-order (gradient) and second-order (Hessian) derivatives of the nonlinear objective function. The volume and surface optimization algorithms are modified such that surface constraints and mesh validity are satisfied. We also propose a simple and efficient Hessian modification method when the Hessian matrix is not positive definite. We demonstrate our approach by comparing our method with a popular nonlinear conjugate gradient method in terms of both efficiency and mesh quality.