Publications

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A well-known strategy for building effective preconditioners for higher-order discretizations of some PDEs, such as Poisson's equation, is to leverage effective preconditioners for their low-order analogs. In this work, we show that high-quality preconditioners can also be derived for the Taylor–Hood discretization of the Stokes equations in much the same manner. In particular, we investigate the use of geometric multigrid based on the (Formula presented.) discretization of the Stokes operator as a preconditioner for the (Formula presented.) discretization of the Stokes system. We utilize local Fourier analysis to optimize the damping parameters for Vanka and Braess–Sarazin relaxation schemes and to achieve robust convergence. These results are then verified and compared against the measured multigrid performance. While geometric multigrid can be applied directly to the (Formula presented.) system, our ultimate motivation is to apply algebraic multigrid within solvers for (Formula presented.) systems via the (Formula presented.) discretization, which will be considered in a companion paper.

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In this article, we present a general methodology to combine the Discontinuous PetrovGalerkin (DPG) method in space and time in the context of methods of lines for transient advection-reaction problems. We first introduce a semidiscretization in space with a DPG method redefining the ideas of optimal testing and practicality of the method in this context. Then, we apply the recently developed DPG-based time-marching scheme, which is of exponential-type, to the resulting system of Ordinary Differential Equations (ODEs). We also discuss how to efficiently compute the action of the exponential of the matrix coming from the space semidiscretization without assembling the full matrix. Finally, we verify the proposed method for 1D+time advection-reaction problems showing optimal convergence rates for smooth solutions and more stable results for linear conservation laws comparing to the classical exponential integrators.

Entangling gates in trapped-ion quantum computers are most often applied to stationary ions with initial motional distributions that are thermal and close to the ground state, while those demonstrations that involve transport generally use sympathetic cooling to reinitialize the motional state prior to applying a gate. Future systems with more ions, however, will face greater nonthermal excitation due to increased amounts of ion transport and exacerbated by longer operational times and variations over the trap array. In addition, pregate sympathetic cooling may be limited due to time costs and laser access constraints. In this paper, we analyze the impact of such coherent motional excitation on entangling-gate error by performing simulations of Mølmer-Sørenson (MS) gates on a pair of trapped-ion qubits with both thermal and coherent excitation present in a shared motional mode at the start of the gate. We quantify how a small amount of coherent displacement erodes gate performance in the presence of experimental noise, and we demonstrate that adjusting the relative phase between the initial coherent displacement and the displacement induced by the gate or using Walsh modulation can suppress this error. We then use experimental data from transported ions to analyze the impact of coherent displacement on MS-gate error under realistic conditions.

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In this paper, we develop an algorithm to efficiently solve risk-averse optimization problems posed in reflexive Banach space. Such problems often arise in many practical applications as, e.g., optimization problems constrained by partial differential equations with uncertain inputs. Unfortunately, for many popular risk models including the coherent risk measures, the resulting risk-averse objective function is nonsmooth. This lack of differentiability complicates the numerical approximation of the objective function as well as the numerical solution of the optimization problem. To address these challenges, we propose a primal–dual algorithm for solving large-scale nonsmooth risk-averse optimization problems. This algorithm is motivated by the classical method of multipliers and by epigraphical regularization of risk measures. As a result, the algorithm solves a sequence of smooth optimization problems using derivative-based methods. We prove convergence of the algorithm even when the subproblems are solved inexactly and conclude with numerical examples demonstrating the efficiency of our method.

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In this paper, we propose a hybrid method that uses stochastic and deterministic search to compute the maximum likelihood estimator of a low-rank count tensor with Poisson loss via state-of-theart local methods. Our approach is inspired by Simulated Annealing for global optimization and allows for fine-grain parameter tuning as well as adaptive updates to algorithm parameters. We present numerical results that indicate our hybrid approach can compute better approximations to the maximum likelihood estimator with less computation than the state-of-the-art methods by themselves.

Social systems are uniquely complex and difficult to study, but understanding them is vital to solving the world’s problems. The Ground Truth program developed a new way of testing the research methods that attempt to understand and leverage the Human Domain and its associated complexities. The program developed simulations of social systems as virtual world test beds. Not only were these simulations able to produce data on future states of the system under various circumstances and scenarios, but their causal ground truth was also explicitly known. Research teams studied these virtual worlds, facilitating deep validation of causal inference, prediction, and prescription methods. The Ground Truth program model provides a way to test and validate research methods to an extent previously impossible, and to study the intricacies and interactions of different components of research.

A major challenge in shape optimization is the coupling of finite element method (FEM) codes in a way that facilitates efficient computation of shape derivatives. This is particularly difficult with multiphysics problems involving legacy codes, where the costs of implementing and maintaining shape derivative capabilities are prohibitive. The volume and boundary methods are two approaches to computing shape derivatives. Each has a major drawback: the boundary method is less accurate, while the volume method is more invasive to the FEM code. We introduce the strip method, which computes shape derivatives on a strip adjacent to the boundary. The strip method makes code coupling simple. Like the boundary method, it queries the state and adjoint solutions at quadrature nodes, but requires no knowledge of the FEM code implementations. At the same time, it exhibits the higher accuracy of the volume method. As an added benefit, its computational complexity is comparable to that of the boundary method, that is, it is faster than the volume method. We illustrate the benefits of the strip method with numerical examples.

A major challenge in shape optimization is the coupling of finite element method (FEM) codes in a way that facilitates efficient computation of shape derivatives. This is particularly difficult with multiphysics problems involving legacy codes, where the costs of implementing and maintaining shape derivative capabilities are prohibitive. The volume and boundary methods are two approaches to computing shape derivatives. Each has a major drawback: the boundary method is less accurate, while the volume method is more invasive to the FEM code. We introduce the strip method, which computes shape derivatives on a strip adjacent to the boundary. The strip method makes code coupling simple. Like the boundary method, it queries the state and adjoint solutions at quadrature nodes, but requires no knowledge of the FEM code implementations. At the same time, it exhibits the higher accuracy of the volume method. As an added benefit, its computational complexity is comparable to that of the boundary method, that is, it is faster than the volume method. We illustrate the benefits of the strip method with numerical examples.

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In April 5-7, 2022, Sandia National Laboratories hosted a second virtual workshop to further explore the potential for developing AI-enhanced co-design for microelectronics (AICoM). This second piece in an ongoing workshop series again brought together two themes. The first theme, co-design for next generation microelectronics, was drawn from the 2018 Department of Energy Office of Science (DOE SC) “Basic Research Needs for Microelectronics” (BRN) report (DOE/SC, 2018, 2021), which called for a “fundamental rethinking” of the traditional design approach to microelectronics, in which subject matter experts (SMEs) in each microelectronics discipline (materials, devices, circuits, algorithms, etc.) work near-independently. Instead, the BRN called for a non-hierarchical, egalitarian vision of co-design, wherein “each scientific discipline informs and engages the others” in “parallel but intimately networked efforts to create radically new capabilities.” The second theme, exploiting and advancing artificial intelligence (AI) to support co-design for microelectronics, acknowledges the continuing breakthroughs in AI that are currently enhancing and accelerating solutions to traditional design problems in materials synthesis and processing, circuit design, and electronic design automation (EDA).