The generation of locally adapted conforming tetrahedral meshes is an important component of many modern algorithms in the finite element solution of partial differential equations. Typically, such meshes are produced by starting with a coarse initial tetrahedral mesh, followed by mesh adaption on demand over space and time. During the calculation of a time step, a combination of error estimation and a refinement mechanism to deliver higher accuracy can be obtained, if needed, by increasing the spatial resolution. Features for refinement based on different kinds of error estimations and refinement methods applied to an initial mesh have been added to the three-dimensional Finite Element Diffusion and Oxidation Simulator (FEDOS). The implementation of copper and low-K materials as major components of interconnect structures has resulted in the necessity to create new current design rules to ensure chip immunity to electromigration-induced failures. This practical demand causes an enormous interest in understanding the fundamental reliability properties of interconnect copper metalization. Modeling the micro-mechanics of electromigration-caused void evolution is a long-standing scientific problem. Diffuse interface models circumvent computationally costly surface tracking by application of a smooth order parameter field to represent the void structures. We solve the diffuse interface model governing equation with a finite element scheme coupled with a powerful mesh adaptation algorithm. The robustness of the developed finite element approach with respect to the underlying mesh structure enables the efficient simulation of the damage induced by electromigration in complex interconnect geometries. Based on FEDOS a new simulator has been developed and investigated to fulfill almost all demands of modern electromigration simulations. Three dimensional k-space tessellation plays a more and more important role in the area of the full band Monte Carlo method, which provides us with accurate material properties and device simulations. Due to the high symmetry of the Brillouin zone, the discretization of the k-space domain can be reduced to a geometric figure which is called irreducible wedge. Several discretization methods based on different mesh generation regimes are proposed in literature. One very common method for three-dimensional mesh generation is the so-called octtree method. The basic idea behind this method is to divide the whole domain to be meshed into cubes and afterwards divide these cubes into tetrahedrons. This algorithm sounds very easy and fast for simple geometries, but on a closer look, many difficulties appear. The most flexible and therefore best choice is to use an unstructured tetrahedron-based mesh which can be shaped according to the needs of full band Monte Carlo simulators. Different mesh generation methods have been developed, implemented, investigated, and added to the Vienna Monte Carlo simulator (VMC).