Unified Space-Time Isogeometric Collocation Methods for Efficient Thermal Analysis and Simulation with Applications in Additive Manufacturing

Description

This project investigates and develops alternative methods for producing unified space time solutions based on isogeometric collocation methods (ST-IGA-C). Both spatial and time dimensions are integrated as a single extended computation space. The computation space and the solution space are further represented using the same non-uniform rational B-splines (NURBS) basis functions. Isogeometric collocation methods (IGA-C) are finally applied for producing the IGA solutions. The main idea of IGA-C rests on the discretization of the governing partial differential equations (PDEs) in strong form at designated collocation positions. The use of the IGA-C method leads to the use of a reduced number of evaluations needed for solution matrix formation to only one-perdegree of freedom and further reduces the computational cost for isogeometric analysis. In addition, other algorithms based on blockwise solutions and smooth adaptive knots will also been developed for producing efficient unified space-time IGA-C solutions. Main areas of research in the proposed project include (1) the development of a general framework on isogeometric collocation methods for unified space-time IGA-C solutions using NURBS, subdivision schemes and other compatible spline spaces for unstructured quadrilateral meshes, (2) efficient blockwise solutions along the time dimension for unified space-time IGA-C solutions, (3) smooth adaptive knots for field-aligned space-time IGA-C solutions with improved per-degree-of-freedom accuracy for application specific solutions, and (4) application of the resulting parameterization in thermal analysis and simulation with a particular emphasis on process modeling and simulation for 3D/4D printing. The proposed methods will contribute to isogeometric analysis with added capability in producing efficient unified space-time IGA-C solutions and with extended applications in time-dependent thermal analysis and simulation, especially in process simulation and optimization for metal additive manufacturing and other 3D/4D printing processes to be addressed in the project. The research outcomes can also be further extended for simulation in mechanics of soft and responsive materials and for producing efficient time-dependent solutions for many other applications in connection with heat transfer and fluid flow simulation.