A theoretical and numerical investigation of a family of immersed finite element methods

In this article we consider the widely used immersed finite element method (IFEM), in both explicit and implicit form, and its relationship to our more recent one-field fictitious domain method (FDM). We review and extend the formulation of these methods, based upon an operator splitting scheme, in order to demonstrate that both the explicit IFEM and the one-field FDM can be regarded as particular linearizations of the fully implicit IFEM. However, the one-field FDM can be shown to be more robust than the explicit IFEM and can simulate a wider range of solid parameters with a relatively large time step. In addition, it can produce results almost identical to the implicit IFEM but without iteration inside each time step. We study the effect on these methods of variations in viscosity and density of fluid and solid materials. The advantages of the one-field FDM within the IFEM framework are illustrated through a selection of parameter sets for two benchmark cases

Bone Marrow Transplantation for Feline Mucopolysaccharidosis I

Severe mucopolysaccharidosis type I (MPS I) is a fatal neuropathic lysosomal storage disorder with significant skeletal involvement. Treatment involves bone marrow transplantation (BMT), and although effective, is suboptimal, due to treatment sequelae and residual disease. Improved approaches will need to be tested in animal models and compared to BMT. Herein we report on bone marrow transplantation to treat feline mucopolysaccharidosis I (MPS I). Five MPS I stably engrafted kittens, transplanted with unfractionated bone marrow (6.3 × 107–1.1 × 109 nucleated bone marrow cells per kilogram) were monitored for 13–37 months post-engraftment. The tissue total glycosaminoglycan (GAG) content was reduced to normal levels in liver, spleen, kidney, heart muscle, lung, and thyroid. Aorta GAG content was between normal and affected levels. Treated cats had a significant decrease in the brain GAG levels relative to untreated MPS I cats and a paradoxical decrease relative to normal cats. The α-l-iduronidase (IDUA) activity in the livers and spleens of transplanted MPS I cats approached heterozygote levels. In kidney cortex, aorta, heart muscle, and cerebrum, there were decreases in GAG without significant increases in detectable IDUA activity. Treated animals had improved mobility and decreased radiographic signs of disease. However, significant pathology remained, especially in the cervical spine. Corneal clouding appeared improved in some animals. Immunohistochemical and biochemical analysis documented decreased central nervous system ganglioside storage. This large animal MPS I study will serve as a benchmark of future therapies designed to improve on BMT

An energy stable one-field monolithic arbitrary Lagrangian-Eulerian formulation for fluid-structure interaction

In this article we present a one-field monolithic finite element method in the Arbitrary Lagrangian–Eulerian (ALE) formulation for Fluid–Structure Interaction (FSI) problems. The method only solves for one velocity field in the whole FSI domain, and it solves in a monolithic manner so that the fluid solid interface conditions are satisfied automatically. We prove that the proposed scheme is unconditionally stable, through energy analysis, by utilising a conservative formulation and an exact quadrature rule. We implement the algorithm using both F-scheme and D-scheme, and demonstrate that the former has the same formulation in two and three dimensions. Finally several numerical examples are presented to validate this methodology, including combination with remesh techniques to handle the case of very large solid displacement

A Multilevel Approach for Obtaining Locally Optimal Finite Element Meshes

In this paper we consider the adaptive finite element solution of a general class of variational problems using a combination of node insertion, node movement and edge swapping. The adaptive strategy that is proposed is based upon the construction of a hierarchy of locally optimal meshes starting with a coarse grid for which the location and connectivity of the nodes is optimized. This grid is then locally refined and the new mesh is optimized in the same manner. Results presented indicate that this approach is able to produce better meshes than those possible by more conventional adaptive strategies and in a relatively efficient manner. 1 Introduction Automatic mesh generation is an important computational tool for the finite element analysis of a wide variety of engineering problems ranging from structural analysis through to computational fluid dynamics for example. For many of these problems the use of unstructured grids offers many advantages over structured grids, such as..