2021-09-142021-09-142021-082021-08August 202https://hdl.handle.net/2346/87905In this dissertation, two novel applications of finite element method(FEM) are presented. In Chapter I, we propose a novel hybrid method that incorporates the Arbitrary Lagrangian-Eulerian (ALE) approach into material point method(MPM) for fluid-structure interaction(FSI) problems. In this formulation, fluid motion is described by Navier- Stokes equations formulated in ALE form. Variational formulation concerning the fluid is supported by the stabilizing residual- based variational multiscale(RBVM) method. Variational structural equations concerning the solid are assembled using MPM. We let fluid-solid interface cut the elements arbitrarily. To ensure well system conditioning and stability of the resulting system irrespective of how the interface intersects the cut elements, face-oriented ghost penalty stabilization is applied on the cut element faces. Continuity of velocities and normal stresses on the boundary is weakly enforced by the Nitsche’s method. The advantage of our hybrid approach is that it provides a framework which eliminates the mesh entanglement issues encountered in ALE based finite element methods for fluid structure interaction problems involving large structural deformation. In Chapter II, we derive a full 3-dimensional (3-D) model of inhomogeneous -- anisotropic diffusion in a tumor region coupled to a binary population model, which simulates in vivo scenarios faster than traditional cell-line tests. The diffusion tensors are acquired using Diffusion Tensor Magnetic Resonance Imaging (DTI) from a patient diagnosed with glioblastoma multiform (GBM). Then we numerically simulate the full model with FEM and produce drug concentration heat maps, apoptosis hotspots, and dose-response curves. Finally, predictions are made about optimal injection locations and volumes, which are presented in a form that can be employed by doctors and oncologists.application/pdfengFluid Structure InteractionMaterial Point MethodDiffusion Tensor ImagingTumorThesis2021-09-14Access is not restricted.