Related papers: Space-time multilevel quadrature methods and their…
Multidimensional phase space integrals must be calculated in order to obtain predictions for total or differential cross sections, or to simulate unweighted events of multiparticle reactions. The corresponding matrix elements, already in…
Cardiovascular simulations are increasingly used for non-invasive diagnosis of cardiovascular disease, to guide treatment decisions, and in the design of medical devices. Quantitative assessment of the variability of simulation outputs due…
We present a Virtual Element Method (VEM) for a nonlocal reaction-diffusion system of the cardiac electric field. To this system, we analyze an $H^1(\Omega)$-conforming discretization by means of VEM which can make use of general polygonal…
We study quasi-Monte Carlo (QMC) integration over the multi-dimensional unit cube in several weighted function spaces with different smoothness classes. We consider approximating the integral of a function by the median of several integral…
Practical structural engineering problems often exhibit a significant degree of uncertainty in the material properties being used, the dimensions of the modeled structures, etc. In this paper, we consider a cantilever beam and a beam…
We introduce a general Monte Carlo scheme for achieving atomistic simulations with monoelectronic Hamiltonians including the thermalization of both nuclear and electronic degrees of freedom. The kinetic Monte Carlo algorithm is used to…
The segmentation and classification of cardiac magnetic resonance imaging are critical for diagnosing heart conditions, yet current approaches face challenges in accuracy and generalizability. In this study, we aim to further advance the…
We present the preliminary tests on two modifications of the Hybrid Monte Carlo (HMC) algorithm. Both algorithms are designed to travel much farther in the Hamiltonian phase space for each trajectory and reduce the autocorrelations among…
A real-time path integral Monte Carlo approach is developed to study the dynamics in a many-body quantum system until reaching a nonequilibrium stationary state. The approach is based on augmenting an exact reduced equation for the…
We present a mathematical framework for constructing and analyzing parallel algorithms for lattice Kinetic Monte Carlo (KMC) simulations. The resulting algorithms have the capacity to simulate a wide range of spatio-temporal scales in…
In the design of stellarators, energetic particle confinement is a critical point of concern which remains challenging to study from a numerical point of view. Standard Monte Carlo analyses are highly expensive because a large number of…
We propose four novel mathematical models, describing the microscopic mechanisms of force generation in the cardiac muscle tissue, which are suitable for multiscale numerical simulations of cardiac electromechanics. Such models are based on…
Hypertrophic cardiomyopathy (HCM) requires accurate risk stratification to inform decisions regarding ICD therapy and follow-up management. Current established models, such as the European Society of Cardiology (ESC) score, exhibit moderate…
We propose a multi-index algorithm for the Monte Carlo (MC) discretization of a linear, elliptic PDE with affine-parametric input. We prove an error vs. work analysis which allows a multi-level finite-element approximation in the physical…
The Multilevel Monte Carlo method is an efficient variance reduction technique. It uses a sequence of coarse approximations to reduce the computational cost in uncertainty quantification applications. The method is nowadays often considered…
The forward problem in electrocardiology, computing body surface potentials from cardiac electrical activity, is traditionally solved using physics-based models such as the bidomain or monodomain equations. While accurate, these approaches…
When calculating satellite trajectories in low-earth orbit, engineers need to adequately estimate aerodynamic forces. But to this day, obtaining the drag acting on the complicated shapes of modern spacecraft suffers from many sources of…
We present a new approach to the study of equilibrium properties in many-body quantum physics. Our method takes inspiration from Density Matrix Quantum Monte Carlo and incorporates new crucial features. First of all, the dynamics is…
Computational cardiac modelling is a mature area of biomedical computing, and is currently evolving from a pure research tool to aiding in clinical decision making. Assessing the reliability of computational model predictions is a key…
In the framework of accurate and efficient segregated schemes for 3D cardiac electromechanics and 0D cardiovascular models, we propose here a novel numerical approach to address the coupled 3D-0D problem introduced in Part I of this…