Computer Science

We present an enhanced version of the parametric nonlinear reduced order model for shape imperfections in structural dynamics we studied in a previous work [1]. The model is computed intrusively and with no training using information about the nominal geometry of the structure and some user-defined displacement fields representing shape defects, i.e. small deviations from the nominal geometry parametrized by their respective amplitudes. The linear superposition of these artificial displacements describe the defected geometry and can be embedded in the strain formulation in such a way that, in the end, nonlinear internal elastic forces can be expressed as a polynomial function of both these defect fields and the actual displacement field. This way, a tensorial representation of the internal forces can be obtained and, owning the reduction in size of the model given by a Galerkin projection, high simulation speed-ups can be achieved. We show that by adopting a rigorous deformation framework we are able to achieve better accuracy as compared to the previous work. In particular, exploiting Neumann expansion in the definition of the Green-Lagrange strain tensor, we show that our previous model is a lower order approximation with respect to the one we present now. Two numerical examples of a clamped beam and a MEMS gyroscope finally demonstrate the benefits of the method in terms of speed and increased accuracy.

Computational models are increasingly used for diagnosis and treatment of cardiovascular disease. To provide a quantitative hemodynamic understanding that can be effectively used in the clinic, it is crucial to quantify the variability in the outputs from these models due to multiple sources of uncertainty. To quantify this variability, the analyst invariably needs to generate a large collection of high-fidelity model solutions, typically requiring a substantial computational effort. In this paper, we show how an explicit-in-time ensemble cardiovascular solver offers superior performance with respect to the embarrassingly parallel solution with implicit-in-time algorithms, typical of an inner-outer loop paradigm for non-intrusive uncertainty propagation. We discuss in detail the numerics and efficient distributed implementation of a segregated FSI cardiovascular solver on both CPU and GPU systems, and demonstrate its applicability to idealized and patient-specific cardiovascular models, analyzed under steady and pulsatile flow conditions.

Integrated models for fluid-driven fracture propagation and general multiphase flow in porous media are valuable to the study and engineering of several systems, including hydraulic fracturing, underground disposal of waste, and geohazard mitigation across such applications. This work extends the coupled model multiphase flow and poromechanical model of \cite{ren2018embedded} to admit fracture propagation (FP). The coupled XFEM-EDFM scheme utilizes a separate fracture mesh that is embedded on a static background mesh. The onset and dynamics of fracture propagation (FP) are governed by the equivalent stress intensity factor (SIF) criterion. A domain-integral method (J integral) is applied to compute this information. An adaptive time-marching scheme is proposed to rapidly restrict and grow temporal resolution to match the underlying time-scales. The proposed model is verified with analytical solutions, and shows the capability to accurately and adaptively co-simulate fluid transport and deformation as well as the propagation of multiple fractures.

Mathematical modeling of cardiac function can provide augmented simulation-based diagnosis tool for complementing and extending human understanding of cardiac diseases which represent the most common cause of worldwide death. As the realistic starting-point for developing an unified meshless approach for total heart modeling, herein we propose an integrative smoothed particle hydrodynamics (SPH) framework for addressing the simulation of the principle aspects of cardiac function, including cardiac electrophysiology, passive mechanical response and electromechanical coupling. To that end, several algorithms, e.g., splitting reaction-by-reaction method combined with quasi-steady-state (QSS) solver , anisotropic SPH-diffusion discretization and total Lagrangian SPH formulation, are introduced and exploited for dealing with the fundamental challenges of developing integrative SPH framework for simulating cardiac function, namely, (i) the correct capturing of the stiff dynamics of the transmembrane potential and the gating variables , (ii) the stable predicting of the large deformations and the strongly anisotropic behavior of the myocardium, and (iii) the proper coupling of electrophysiology and tissue mechanics for electromechanical feedback. A set of numerical examples demonstrate the effectiveness and robustness of the present SPH framework, and render it a potential and powerful alternative that can augment current lines of total cardiac modeling and clinical applications.

In this paper, we propose an iterative splitting method to solve the partial differential equations in option pricing problems. We focus on the Heston stochastic volatility model and the derived two-dimensional partial differential equation (PDE). We take the European option as an example and conduct numerical experiments using different boundary conditions. The iterative splitting method transforms the two-dimensional equation into two quasi one-dimensional equations with the variable on the other dimension fixed, which helps to lower the computational cost. Numerical results show that the iterative splitting method together with an artificial boundary condition (ABC) based on the method by Li and Huang (2019) gives the most accurate option price and Greeks compared to the classic finite difference method with the commonly-used boundary conditions in Heston (1993).

In modelling of chemical, physical or biological systems it may occur that the coefficients, multiplying various terms in the equation of interest, differ greatly in magnitude, if a particular system of units is used. Such is, for instance, the case of the Population Balance Equations (PBE) proposed to model the Latex Particles Morphology formation. The obvious way out of this difficulty is the use of dimensionless scaled quantities, although often the scaling procedure is not unique. In this paper, we introduce a conceptually new general approach, called Optimal Scaling (OS). The method is tested on the known examples from classical and quantum mechanics, and applied to the Latex Particles Morphology model, where it allows us to reduce the variation of the relevant coefficients from 49 to just 4 orders of magnitudes. The PBE are then solved by a novel Generalised Method Of Characteristics, and the OS is shown to help reduce numerical error, and avoid unphysical behaviour of the solution. Although inspired by a particular application, the proposed scaling algorithm is expected find application in a wide range of chemical, physical and biological problems.

In this article, we present the development of a two-step optimization framework to deal with the design and selection of aircraft departure routes and the allocation of flights among these routes. The aim of the framework is to minimize cumulative noise annoyance and fuel burn. In the first step of the framework, multi-objective trajectory optimization is used to compute and store a set of routes that will serve as inputs in the second step. In the second step, the selection of routes from the set of pre-computed optimal routes and the optimal allocation of flights among these routes are conducted simultaneously. To validate the proposed framework, we also conduct an analysis involving an integrated (one-step) approach, in which both trajectory optimization and route allocation are formulated as a single optimization problem. A comparison of both approaches is then performed, and their advantages and disadvantages are identified. The performance and capabilities of the present framework are demonstrated using a case study at Amsterdam Airport Schiphol in The Netherlands. The numerical results show that the proposed framework can generate solutions which can achieve a reduction in the number of people annoyed of up to 31% and a reduction in fuel consumption of 7.3% relative to the reference case solution.

The study of tunnel failure characteristics under the load of external explosion source is an important problem in tunnel design and protection, in particular, it is of great significance to construct an intelligent topological feature description of the tunnel failure process. The failure characteristics of tunnels under explosive loading are described by using discrete element method and persistent homology-based machine learning. Firstly, the discrete element model of shallow buried tunnel was established in the discrete element software, and the explosive load was equivalent to a series of uniformly distributed loads acting on the surface by Saint-Venant principle, and the dynamic response of the tunnel under multiple explosive loads was obtained through iterative calculation. The topological characteristics of surrounding rock is studied by persistent homology-based machine learning. The geometric, physical and interunit characteristics of the tunnel subjected to explosive loading are extracted, and the nonlinear mapping relationship between the topological quantity of persistent homology, and the failure characteristics of the surrounding rock is established, and the results of the intelligent description of the failure characteristics of the tunnel are obtained. The research shows that the length of the longest Betty 1 bar code is closely related to the stability of the tunnel, which can be used for effective early warning of the tunnel failure, and an intelligent description of the tunnel failure process can be established to provide a new idea for tunnel engineering protection.

This paper proposes a method to detect bank frauds using a mixed approach combining a stochastic intensity model with the probability of fraud observed on transactions. It is a dynamic unsupervised approach which is able to predict financial frauds. The fraud prediction probability on the financial transaction is derived as a function of the dynamic intensities. In this context, the Kalman filter method is proposed to estimate the dynamic intensities. The application of our methodology to financial datasets shows a better predictive power in higher imbalanced data compared to other intensity-based models.

The coupled simulations of dynamic interactions between the well, hydraulic fractures and reservoir have significant importance in some areas of petroleum reservoir engineering. Several approaches to the problem of coupling between the numerical models of these parts of the full system have been developed in the industry in past years. One of the possible approaches allowing formulation of the problem as a fixed-point problem is studied in the present work. Accelerated Anderson's and Aitken's fixed-point algorithms are applied to the coupling problem. Accelerated algorithms are compared with traditional Picard iterations on the representative set of test cases including ones remarkably problematic for coupling. Relative performance is measured, and the robustness of the algorithms is tested. Accelerated algorithms enable a significant (up to two orders of magnitude) performance boost in some cases and convergent solutions in the cases where simple Picard iterations fail. Based on the analysis, we provide recommendations for the choice of the particular algorithm and tunable relaxation parameter depending on anticipated complexity of the problem.