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Due to undecidability and complexity of first-order logic, SMT solvers may not terminate on some problems or require a very long time. When this happens, one would like to find the reasons why the solver fails. To this end, we have designed…
We present Decapodes, a diagrammatic tool for representing, composing, and solving partial differential equations. Decapodes provides an intuitive diagrammatic representation of the relationships between variables in a system of equations,…
The goal of this work is to parallelize the multistep scheme for the numerical approximation of the backward stochastic differential equations (BSDEs) in order to achieve both, a high accuracy and a reduction of the computation time as…
Emerging immersive display technologies efficiently utilize resources with perceptual graphics methods such as foveated rendering and denoising. Running multiple perceptual graphics methods challenges devices with limited power and…
We present a simple to use, yet powerful code package called NLSEmagic to numerically integrate the nonlinear Schr\"odinger equation in one, two, and three dimensions. NLSEmagic is a high-order finite-difference code package which utilizes…
A standard quadratic program is an optimization problem that consists of minimizing a (nonconvex) quadratic form over the unit simplex. We focus on reformulating a standard quadratic program as a mixed integer linear programming problem. We…
This is the fourth installment in our series on implementing the discontinuous Galerkin (DG) method as an open source MATLAB /GNU Octave toolbox. Similarly to its predecessors, this part presents new features for application developers…
We report on the development of a general tool called ExSched, implemented as a plug-in for Microsoft Excel, for solving a class of constraint satisfaction problems. The traditional spreadsheet paradigm is based on attaching arithmetic…
Building interactive tools to support data analysis is hard because it is not always clear what to build and how to build it. To address this problem, we present Precision Interfaces, a semi-automatic system to generate task-specific data…
This article presents a comparison of various implementations of the Lattice Discrete Particle Model (LDPM) for the numerical simulation of concrete and other heterogeneous quasibrittle materials. The comparison involves the use of…
In this paper, a novel multigrid method based on Newton iteration is proposed to solve nonlinear eigenvalue problems. Instead of handling the eigenvalue $\lambda$ and eigenfunction $u$ separately, we treat the eigenpair $(\lambda, u)$ as…
This paper describes an updated exponential Fourier based split-step method that can be applied to a greater class of partial differential equations than previous methods would allow. These equations arise in physics and engineering, a…
We present a multirate method that is particularly suited for integrating the systems of Ordinary Differential Equations (ODEs) that arise in step models of surface evolution. The surface of a crystal lattice, that is slightly miscut from a…
Novice programmers often struggle with problem solving due to the high cognitive loads they face. Furthermore, many introductory programming courses do not explicitly teach it, assuming that problem solving skills are acquired along the…
Nonlinear least-squares problems are a special class of unconstrained optimization problems in which their gradient and Hessian have special structures. In this paper, we exploit these structures and proposed a matrix-free algorithm with a…
A monitor is a widely-used concurrent programming abstraction that encapsulates all shared state between threads. Monitors can be classified as being either implicit or explicit depending on the primitives they provide. Implicit monitors…
We develop NL2INTERFACE to explore the potential of generating usable interactive multi-visualization interfaces from natural language queries. With NL2INTERFACE, users can directly write natural language queries to automatically generate a…
The athermal quasistatic deformation method provides an elegant solution to overcome the limitation of short time spans in molecular simulations. It provides overdamped conditions, allowing for the extraction of purely structural responses…
The application of deep learning techniques in software engineering becomes increasingly popular. One key problem is developing high-quality and easy-to-use source code representations for code-related tasks. The research community has…
An efficient method for solving large nonlinear problems combines Newton solvers and Domain Decomposition Methods (DDM). In the DDM framework, the boundary conditions can be chosen to be primal, dual or mixed. The mixed approach presents…