Deformable Simplicial Complexes

In this dissertation we present a novel method for deformable interface tracking in 2D and 3D|deformable simplicial complexes (DSC). Deformable interfaces are used in several applications, such as fluid simulation, image analysis, reconstruction or structural optimization. In the DSC method, the interface (curve in 2D; surface in 3D) is represented explicitly as a piecewise linear curve or surface. However, the domain is also subject to discretization: triangulation in 2D; tetrahedralization in 3D. This way, the interface can be alternatively represented as a set of edges/triangles separating triangles/tetrahedra marked as outside from those marked as inside. Such an approach allows for robust topological adaptivity. Among other advantages of the deformable simplicial complexes there are: space adaptivity, ability to handle and preserve sharp features, possibility for topology control. We demonstrate those strengths in several applications. In particular, a novel, DSC-based fluid dynamics solver has been developed during the PhD project. A special feature of this solver is that due to the fact that DSC maintains an explicit interface representation, surface tension is more easily dealt with. One particular advantage of DSC is the fact that as an alternative to topology adaptivity, topology control is also possible. This is exploited in the construction of cut loci on tori where a front expands from a single point on a torus and stops when it self-intersects

Comparing approaches for numerical modelling of tsunami generation by deformable submarine slides

Tsunami generated by submarine slides are arguably an under-considered risk in comparison to earthquake-generated tsunami. Numerical simulations of submarine slide-generated waves can be used to identify the important factors in determining wave characteristics. Here we use Fluidity, an open source finite element code, to simulate waves generated by deformable submarine slides. Fluidity uses flexible unstructured meshes combined with adaptivity which alters the mesh topology and resolution based on the simulation state, focussing or reducing resolution, when and where it is required. Fluidity also allows a number of different numerical approaches to be taken to simulate submarine slide deformation, free-surface representation, and wave generation within the same numerical framework. In this work we use a multi-material approach, considering either two materials (slide and water with a free surface) or three materials (slide, water and air), as well as a sediment model (sediment, water and free surface) approach. In all cases the slide is treated as a viscous fluid. Our results are shown to be consistent with laboratory experiments using a deformable submarine slide, and demonstrate good agreement when compared with other numerical models. The three different approaches for simulating submarine slide dynamics and tsunami wave generation produce similar waveforms and slide deformation geometries. However, each has its own merits depending on the application. Mesh adaptivity is shown to be able to reduce the computational cost without compromising the accuracy of results

Controlling the Error on Target Motion through Real-time Mesh Adaptation: Applications to Deep Brain Stimulation

We present an error-controlled mesh refinement procedure for needle insertion simulation and apply it to the simulation of electrode implantation for deep brain stimulation, including brain shift. Our approach enables to control the error in the computation of the displacement and stress fields around the needle tip and needle shaft by suitably refining the mesh, whilst maintaining a coarser mesh in other parts of the domain. We demonstrate through academic and practical examples that our approach increases the accuracy of the displacement and stress fields around the needle without increasing the computational expense. This enables real-time simulations. The proposed methodology has direct implications to increase the accuracy and control the computational expense of the simulation of percutaneous procedures such as biopsy, brachytherapy, regional anesthesia, or cryotherapy and can be essential to the development of robotic guidance.Comment: 21 pages, 14 figure

Multifarious Hierarchies of Mechanical Models for Artist Assigned Levels-of-Detail

International audienceWe present a new framework for artist driven level of detail in solid simulations. Simulated objects are simultaneously embedded in several, separately designed deformation models with their own independent degrees of freedom. The models are ordered to apply their deformations hierarchically, and we enforce the uniqueness of the dynamics solutions using a novel kinetic filtering operator designed to ensure that each child only adds detail motion to its parent without introducing redundancies. This new approach allows artists to easily add fine-scale details without introducing unnecessary degrees-of-freedom to the simulation or resorting to complex geometric operations like anisotropic volume meshing. We illustrate the utility of our approach with several detail enriched simulation examples

Animation of deformable bodies with quadratic bézier finite elements

pre-printIn this article, we investigate the use of quadratic finite elements for graphical animation of deformable bodies.We consider both integrating quadratic elements with conventional linear elements to achieve a computationally efficient adaptive-degree simulation framework as well as wholly quadratic elements for the simulation of nonlinear rest shapes. In both cases, we adopt the B´ezier basis functions and employ a co-rotational linear strain formulation. As with linear elements, the co-rotational formulation allows us to precompute per-element stiffness matrices, resulting in substantial computational savings. We present several examples that demonstrate the advantages of quadratic elements in general and our adaptive-degree system in particular. Furthermore, we demonstrate, for the first time in computer graphics, animations of volumetric deformable bodies with nonlinear rest shapes

High-order adaptive time stepping for vesicle suspensions with viscosity contrast

We construct a high-order adaptive time stepping scheme for vesicle suspensions with viscosity contrast. The high-order accuracy is achieved using a spectral deferred correction (SDC) method, and adaptivity is achieved by estimating the local truncation error with the numerical error of physically constant values. Numerical examples demonstrate that our method can handle suspensions with vesicles that are tumbling, tank-treading, or both. Moreover, we demonstrate that a user-prescribed tolerance can be automatically achieved for simulations with long time horizons

Outflow boundary conditions for 3D simulations of non-periodic blood flow and pressure fields in deformable arteries

The simulation of blood flow and pressure in arteries requires outflow boundary conditions that incorporate models of downstream domains. We previously described a coupled multidomain method to couple analytical models of the downstream domains with 3D numerical models of the upstream vasculature. This prior work either included pure resistance boundary conditions or impedance boundary conditions based on assumed periodicity of the solution. However, flow and pressure in arteries are not necessarily periodic in time due to heart rate variability, respiration, complex transitional flow or acute physiological changes. We present herein an approach for prescribing lumped parameter outflow boundary conditions that accommodate transient phenomena. We have applied this method to compute haemodynamic quantities in different physiologically relevant cardiovascular models, including patient-specific examples, to study non-periodic flow phenomena often observed in normal subjects and in patients with acquired or congenital cardiovascular disease. The relevance of using boundary conditions that accommodate transient phenomena compared with boundary conditions that assume periodicity of the solution is discussed

Seamless Adaptivity of Elastic Models

International audienceA new adaptive model for viscoelastic solids is presented. Unlike previous approaches, it allows seamless transitions, and simplifications in deformed states. The deformation field is generated by a set of physically animated frames. Starting from a fine set of frames and mechanical energy integration points, the model can be coarsened by attaching frames to others, and merging integration points. Since frames can be attached in arbitrary relative positions, simplifications can occur seamlessly in deformed states, without returning to the original shape, which can be recovered later after refinement. We propose a new class of velocity-based simplification criterion based on relative velocities. Integration points can be merged to reduce the computation time even more, and we show how to maintain constant elastic forces through the levels of detail. This meshless adaptivity allows significant improvements of computation time