Computational Phase-Field Modeling

11:30AM at REC 114
Professor Hector Gomez, Purdue University
Computational Phase-Field Modeling
Guang Lin

Phase-field modeling refers to a particular mathematical description of a system with evolving interfaces. The key idea is that interfaces are described by a smoothly-changing function, the phase-field, which is defined on a fixed computational domain. The phase-field evolution is typically governed by a higher-order partial differential equation which tracks the so-called diffuse interfaces and encodes the interfacial physics at once. Computational phase-field modeling has been traditionally dominated by classical collocation methods, which have permitted a simple discretization of higher-order operators on simple geometries. In this talk, I will explore the potential of Isogeometric Analysis for computational phase-field modeling. Isogeometric Analysis presents several features which make it naturally well suited for phase-fields, such as for example, globally smooth basis functions on non-trivial geometries, excellent approximability, and robustness for nonlinear problems. I will also introduce our non-linearly stable time integration algorithms. To show the potential of our approach, I will present algorithms and numerical examples for remarkably different problems, boiling, the implosion of a solid structure due to condensation of a complex fluid or elasto-capillarity. Time permitting, I will introduce the concept of variational collocation methods to solve partial-differential equations numerically. Variational collocation retains the properties of the Galerkin method, but its computational cost reduces to one point evaluation per degree of freedom, as in classical collocation methods. This technology is expected to create new opportunities in the field of isogeometric analysis and meshless methods.