Efficient isogeometric thin shell formulations for soft biological materials

This paper presents three different constitutive approaches to model thin rotation-free shells based on the Kirchhoff-Love hypothesis. One approach is based on numerical integration through the shell thickness while the other two approaches do not need any numerical integration and so they are computationally more efficient. The formulation is designed for large deformations and allows for geometrical and material nonlinearities, which makes it very suitable for the modeling of soft tissues. Furthermore, six different isotropic and anisotropic material models, which are commonly used to model soft biological materials, are examined for the three proposed constitutive approaches. Following an isogeometric approach, NURBS-based finite elements are used for the discretization of the shell surface. Several numerical examples are investigated to demonstrate the capabilities of the formulation. Those include the contact simulation during balloon angioplasty.Comment: Typos are removed. Remark 3.4 is added. Eq. (18) in the previous version is removed. Thus, the equations get renumbered. Example 5.5 is updated. Minor typos in Eqs. (17), (80), (145) and (146), are corrected. They do not affect the result

Semi-classical generalized Langevin equation for equilibrium and nonequilibrium molecular dynamics simulation

Molecular dynamics (MD) simulation based on Langevin equation has been widely used in the study of structural, thermal properties of matters in difference phases. Normally, the atomic dynamics are described by classical equations of motion and the effect of the environment is taken into account through the fluctuating and frictional forces. Generally, the nuclear quantum effects and their coupling to other degrees of freedom are difficult to include in an efficient way. This could be a serious limitation on its application to the study of dynamical properties of materials made from light elements, in the presence of external driving electrical or thermal fields. One example of such system is single molecular dynamics on metal surface, an important system that has received intense study in surface science. In this review, we summarize recent effort in extending the Langevin MD to include nuclear quantum effect and their coupling to flowing electrical current. We discuss its applications in the study of adsorbate dynamics on metal surface, current-induced dynamics in molecular junctions, and quantum thermal transport between different reservoirs.Comment: 23 pages, 16 figur

Development and application of unified algorithms for problems in computational science

A framework is presented for developing computationally unified numerical algorithms for solving nonlinear equations that arise in modeling various problems in mathematical physics. The concept of computational unification is an attempt to encompass efficient solution procedures for computing various nonlinear phenomena that may occur in a given problem. For example, in Computational Fluid Dynamics (CFD), a unified algorithm will be one that allows for solutions to subsonic (elliptic), transonic (mixed elliptic-hyperbolic), and supersonic (hyperbolic) flows for both steady and unsteady problems. The objectives are: development of superior unified algorithms emphasizing accuracy and efficiency aspects; development of codes based on selected algorithms leading to validation; application of mature codes to realistic problems; and extension/application of CFD-based algorithms to problems in other areas of mathematical physics. The ultimate objective is to achieve integration of multidisciplinary technologies to enhance synergism in the design process through computational simulation. Specific unified algorithms for a hierarchy of gas dynamics equations and their applications to two other areas: electromagnetic scattering, and laser-materials interaction accounting for melting

Foreword Special Issue on "New Simulation Methodologies for Next-Generation TCAD Tools"

Technology computer-aided design (TCAD) is an integral part of the development process of semiconductor technologies and devices, a field which has become increasingly complex and heterogeneous. Processing of integrated circuits requires nowadays over 400 process steps, and the resulting devices often have an intricate 3-D structure and contain various specifically designed materials. The full device behavior can only be understood by considering effects on all length scales from atomistic (material properties, interfaces, defects, and so on), to nanometric (quantum confinement, non-bulk properties, tunneling, ballistic transport, and so on), to full-chip dimensions (strain, heat transport, and so on), and time scales from femtoseconds (scattering, ferroelectric switching time, and so on) to seconds (trapping times, degradation, and so on). Voltages, currents, and charges have been scaled to such low levels that statistical effects and process variations have a strong impact. Devices based on new materials (e.g., 2-D crystals) and physical principles (ferroelectrics, magnetic materials, qubits, and so on) challenge standard TCAD approaches. While the simulation methods developed by the physics community can describe the basic device behavior, they often lack important simulation capabilities like, for example, transient simulations or integration with other TCAD tools, and are often too slow for daily use. Due to the complexity of semiconductor technology, it becomes more and more difficult to assess the impact of a change in processing or device structure on circuit performance by looking at a single aspect of an isolated device under idealized conditions. Instead, a TCAD tool chain is required which can handle realistic device structures embedded in a chip environment. New methodologies are required for all aspects of TCAD to ensure an efficient tool chain covering from atomistic effects to circuit behavior based on flexible simulation models that can handle new materials, device principles, and the ensuing large-scale simulations and that make use of artificial intelligence for well-chosen (sub)routines to decrease the overall simulation time. This Special Issue features six invited and 18 regular papers that address these problems

Capture and Modeling of Non-Linear Heterogeneous Soft Tissue

This paper introduces a data-driven representation and modeling technique for simulating non-linear heterogeneous soft tissue. It simplifies the construction of convincing deformable models by avoiding complex selection and tuning of physical material parameters, yet retaining the richness of non-linear heterogeneous behavior. We acquire a set of example deformations of a real object, and represent each of them as a spatially varying stress-strain relationship in a finite-element model. We then model the material by non-linear interpolation of these stress-strain relationships in strain-space. Our method relies on a simple-to-build capture system and an efficient run-time simulation algorithm based on incremental loading, making it suitable for interactive computer graphics applications. We present the results of our approach for several non-linear materials and biological soft tissue, with accurate agreement of our model to the measured data.Engineering and Applied Science

Interacting with Acoustic Simulation and Fabrication

Incorporating accurate physics-based simulation into interactive design tools is challenging. However, adding the physics accurately becomes crucial to several emerging technologies. For example, in virtual/augmented reality (VR/AR) videos, the faithful reproduction of surrounding audios is required to bring the immersion to the next level. Similarly, as personal fabrication is made possible with accessible 3D printers, more intuitive tools that respect the physical constraints can help artists to prototype designs. One main hurdle is the sheer amount of computation complexity to accurately reproduce the real-world phenomena through physics-based simulation. In my thesis research, I develop interactive tools that implement efficient physics-based simulation algorithms for automatic optimization and intuitive user interaction.Comment: ACM UIST 2017 Doctoral Symposiu

Research and Education in Computational Science and Engineering

Over the past two decades the field of computational science and engineering (CSE) has penetrated both basic and applied research in academia, industry, and laboratories to advance discovery, optimize systems, support decision-makers, and educate the scientific and engineering workforce. Informed by centuries of theory and experiment, CSE performs computational experiments to answer questions that neither theory nor experiment alone is equipped to answer. CSE provides scientists and engineers of all persuasions with algorithmic inventions and software systems that transcend disciplines and scales. Carried on a wave of digital technology, CSE brings the power of parallelism to bear on troves of data. Mathematics-based advanced computing has become a prevalent means of discovery and innovation in essentially all areas of science, engineering, technology, and society; and the CSE community is at the core of this transformation. However, a combination of disruptive developments---including the architectural complexity of extreme-scale computing, the data revolution that engulfs the planet, and the specialization required to follow the applications to new frontiers---is redefining the scope and reach of the CSE endeavor. This report describes the rapid expansion of CSE and the challenges to sustaining its bold advances. The report also presents strategies and directions for CSE research and education for the next decade.Comment: Major revision, to appear in SIAM Revie