The concepts of sparse data structures and related algorithms for phase field simulations are discussed. Simulations of polycrystalline grain growth with a conventional phase field method and with sparse data structures are compared. It is shown that memory usage and simulation time scale with the number of nodes but are independent of the number of order parameters when a sparse data structure...

This paper is concerned with the numerical approximation of mean curvature flow t → Ω(t) satisfying an additional inclusion-exclusion constraint Ω1 ⊂ Ω(t) ⊂ Ω2. Classical phase field model to approximate these evolving interfaces consists in solving the AllenCahn equation with Dirichlet boundary conditions. In this work, we introduce a new phase field model, which can be viewed as an Allen Cahn...

Russell J. Hewett [email protected] Imaging and Computing Group Department of Mathematics Massachusetts Institute of Technology Ian Jermyn [email protected] Department of Mathematical Sciences Durham University Michael T. Heath [email protected] Department of Computer Science University of Illinois at Urbana-Champaign Farzad Kamalabadi [email protected] Department of Electrical and Comp...

Predicting and controlling the microstructure evolution within a material are considered as the ‘‘holy grail’’ of materials science and engineering. Many important engineering materials are designed by controlling their phase transformations and microstructure evolution. Examples include the improvement of mechanical properties through solid-state precipitation reactions in Nibased superalloys ...

Phase-field model was employed to quantitatively study the effect of convection on pattern selection and growth rate of 2D and 3D dendrite tip, as well as the effect of the different convection velocity on the dendritic growth. The calculated results show that crystal is asymmetric in the priority direction of growth under flow. The dentritic growth is promoted in the upstream region and suppre...

Phase-retrieval from measured phaseless field data is of interest for various applications including electromagnetic dosimetry, electromagnetic compatibility investigations, near-field to far-field transformations and antenna diagnostics. In this study two phaseretrieval methods, namely the adjoint field method and the phase angle gradient method, are compared using 3D numerical test cases. The...

in this paper, the hartree-fock method has been formulated to investigate some of the ground state properties of quasi-one-dimensional interacting electron gas in the presence of the magnetic field. the bare coulomb interaction between electrons has been assumed. for this system, we have also computed some of its thermodynamic and magnetic properties such as the energy, pressure, incompressibil...