An Additive Schwarz Preconditioner for the Spectral Element Ocean Model Formulation of the Shallow Water Equations

We discretize the shallow water equations with an Adams-Bashford scheme combined with the Crank-Nicholson scheme for the time derivatives and spectral elements for the discretization in space. The resulting coupled system of equations will be reduced to a Schur complement system with a special structure of the Schur complement. This system can be solved with a preconditioned conjugate gradients, where the matrix-vector product is only implicitly given. We derive an overlapping block preconditioner based on additive Schwarz methods for preconditioning the reduced system

Digital twinning of cardiac electrophysiology models from the surface ECG: a geodesic backpropagation approach

The eikonal equation has become an indispensable tool for modeling cardiac electrical activation accurately and efficiently. In principle, by matching clinically recorded and eikonal-based electrocardiograms (ECGs), it is possible to build patient-specific models of cardiac electrophysiology in a purely non-invasive manner. Nonetheless, the fitting procedure remains a challenging task. The present study introduces a novel method, Geodesic-BP, to solve the inverse eikonal problem. Geodesic-BP is well-suited for GPU-accelerated machine learning frameworks, allowing us to optimize the parameters of the eikonal equation to reproduce a given ECG. We show that Geodesic-BP can reconstruct a simulated cardiac activation with high accuracy in a synthetic test case, even in the presence of modeling inaccuracies. Furthermore, we apply our algorithm to a publicly available dataset of a rabbit model, with very positive results. Given the future shift towards personalized medicine, Geodesic-BP has the potential to help in future functionalizations of cardiac models meeting clinical time constraints while maintaining the physiological accuracy of state-of-the-art cardiac models.Comment: 9 pages, 5 figure

Optimal Sizing and Shape Optimization in Structural Mechanics

We consider an industrial application consisting of the mass minimization of a frame in an injection moulding machine. This frame has to compensate the forces acting on the mould inside the machine and has to fulfill certain critical constraints. The deformation of that frame with constant thickness is described by the plain stress state equations for linear elasticity. If the thickness varies then we use a generalized plain stress state with constant thickness in the coarse grid elements. These direct problems are solved by an adaptive multigrid solver. The mass minimization problem leads to a constrained minimization problem for a non-linear functional which will be solved by some standard optimization algorithm which requires the gradients with respect to design parameters. For the shape optimization problem, we assume that the machine components consist of simple geometrical primitives determined by a few design parameters. Therefore, we calculate the gradient in the shape optimization by means of numerical differentiation which requires the solution of approximately 4 direct problems per design parameter. The adaptive solver guarantees the detection of critical regions automatically, and ensures a good approximation to the exact solution of the direct problem. This rather slow approach can be significantly accelerated by using the adjoint method to express the gradient. It will be combined with a direct implementation of several terms that appear after applying the chain rule to the gradient

International conference on computational science, ICCS 2010 data-driven pill monitoring

AbstractWe describe a viable dynamic system to guarantee that pills delivered to a patient are what were prescribed, of sucient quality to be eective, and within the correct time frame. A handheld device that identifies pills is also described that is suitable for use by health care providers. Issues of patient privacy, network security, and interacting with multiple databases are inherent to the entire process

On the Incorporation of Obstacles in a Fluid Flow Problem Using a Navier-Stokes-Brinkman Penalization Approach

Simulating the interaction of fluids with immersed moving solids is playing an important role for gaining a better quantitative understanding of how fluid dynamics is altered by the presence of obstacles and which forces are exerted on the solids by the moving fluid. Such problems appear in various contexts, ranging from numerous technical applications such as turbines to medical problems such as the regulation of hemodyamics by valves. Typically, the numerical treatment of such problems is posed within a fluid structure interaction (FSI) framework. General FSI models are able to capture bidirectional interactions, but are challenging to solve and computationally expensive. Simplified methods offer a possible remedy by achieving better computational efficiency to broaden the scope to demanding application problems with focus on understanding the effect of solids on altering fluid dynamics. In this study we report on the development of a novel method for such applications. In our method rigid moving obstacles are incorporated in a fluid dynamics context using concepts from porous media theory. Based on the Navier-Stokes-Brinkman equations which augments the Navier-Stokes equation with a Darcy drag term our method represents solid obstacles as time-varying regions containing a porous medium of vanishing permeability. Numerical stabilization and turbulence modeling is dealt with by using a residual based variational multiscale formulation. The key advantages of our approach -- computational efficiency and ease of implementation -- are demonstrated by solving a standard benchmark problem of a rotating blood pump posed by the Food and Drug Administration Agency (FDA). Validity is demonstrated by conducting a mesh convergence study and by comparison against the extensive set of experimental data provided for this benchmark

A numerical projection technique for large-scale eigenvalue problems

We present a new numerical technique to solve large-scale eigenvalue problems. It is based on the projection technique, used in strongly correlated quantum many-body systems, where first an effective approximate model of smaller complexity is constructed by projecting out high energy degrees of freedom and in turn solving the resulting model by some standard eigenvalue solver. Here we introduce a generalization of this idea, where both steps are performed numerically and which in contrast to the standard projection technique converges in principle to the exact eigenvalues. This approach is not just applicable to eigenvalue problems encountered in many-body systems but also in other areas of research that result in large scale eigenvalue problems for matrices which have, roughly speaking, mostly a pronounced dominant diagonal part. We will present detailed studies of the approach guided by two many-body models.Comment: 7 pages, 4 figure

Shape of my heart: Cardiac models through learned signed distance functions

The efficient construction of an anatomical model is one of the major challenges of patient-specific in-silico models of the human heart. Current methods frequently rely on linear statistical models, allowing no advanced topological changes, or requiring medical image segmentation followed by a meshing pipeline, which strongly depends on image resolution, quality, and modality. These approaches are therefore limited in their transferability to other imaging domains. In this work, the cardiac shape is reconstructed by means of three-dimensional deep signed distance functions with Lipschitz regularity. For this purpose, the shapes of cardiac MRI reconstructions are learned from public databases to model the spatial relation of multiple chambers in Cartesian space. We demonstrate that this approach is also capable of reconstructing anatomical models from partial data, such as point clouds from a single ventricle, or modalities different from the trained MRI, such as electroanatomical mapping, and in addition, allows us to generate new anatomical shapes by randomly sampling latent vectors

Effects of Sinusoidal Vibrations on the Motion Response of Honeybees

Vibratory signals play a major role in the organization of honeybee colonies. Due to the seemingly chaotic nature of the mechano-acoustic landscape within the hive, it is difficult to understand the exact meaning of specific substrate-borne signals. Artificially generated vibrational substrate stimuli not only allow precise frequency and amplitude control for studying the effects of specific stimuli, but could also provide an interface for human-animal interaction for bee-keeping-relevant colony interventions. We present a simple method for analyzing motion activity of honeybees and show that specifically generated vibrational signals can be used to alter honeybee behavior. Certain frequency-amplitude combinations can induce a significant decrease and other signals might trigger an increase in honeybees’ motion activity. Our results demonstrate how different subtle local modulatory signals on the comb can influence individual bees in the local vicinity of the emitter. Our findings could fundamentally impact our general understanding of a major communication pathway in honeybee colonies. This pathway is based on mechanic signal emission and mechanic proprio-reception of honeybees in the bee colony. It is a candidate to be a technologically accessible gateway into the self-regulated system of the colony and thus may offer a novel information transmission interface between humans and honeybees for the next generation of “smart beehives” in future beekeeping