Sharif Digital Repository

This paper investigates implementation of upwind compact implicit and explicit high-order finite difference schemes for solution of the level set equation. The upwind compact implicit and explicit high-order finite difference schemes are well-known techniques to descritize spatial derivatives for convection term in hyperbolic equations. Applying of upwind high-order schemes on the level set equation leads to less error and CPU time reduction compared to essential non-oscillatory (ENO), weighted essential non-oscillatory schemes (WENO), and even different particle level set methods. The results indicate the error based on area loss decreases drastically with applying high-order upwind,... 

In this paper, an extended finite element method is employed to simulate the presence of discontinuities caused by the contact surface. In X-FEM, the need for mesh adaption to interface is neglected and the process is accomplished by partitioning the domain with some triangular sub-elements whose Gauss points are used for integration of the elements. The modified level set technique and the Heaviside enrichment function are employed to approximate the discontinuous displacement field of elements located on the contact surface. The penalty method is used to impose the contact constraints and establish the non-penetration condition. An efficient numerical algorithm is employed to model the... 

A computational framework was developed to simulate the bone remodelling process as a structural topology optimisation problem. The mathematical formulation of the Level Set technique was extended and then implemented into a coronal plane model of the proximal femur to simulate the remodelling of internal structure and external geometry of bone into the optimal state. Results indicated that the proposed approach could reasonably mimic the major geometrical and material features of the natural bone. Simulation of the internal bone remodelling on the typical gross shape of the proximal femur, resulted in a density distribution pattern with good consistency with that of the natural bone. When...