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We propose a communication- and computation-efficient distributed optimization algorithm using second-order information for solving ERM problems with a nonsmooth regularization term. Current second-order and quasi-Newton methods for this…
Resistive random access memory (ReRAM) is a promising technology that can perform low-cost and in-situ matrix-vector multiplication (MVM) in analog domain. Scientific computing requires high-precision floating-point (FP) processing.…
In this contribution, we are concerned with parameter optimization problems that are constrained by multiscale PDE state equations. As an efficient numerical solution approach for such problems, we introduce and analyze a new relaxed and…
We propose a novel framework for fast integral operations by uncovering hidden geometries in the row and column structures of the underlying operators. This is accomplished through the \texttt{Questionnaire} algorithm, an iterative…
In recent years, randomized algorithms have established themselves as fundamental tools in computational linear algebra, with applications in scientific computing, machine learning, and quantum information science. Many randomized matrix…
This paper focuses on discussing Newton's method and its hybrid with machine learning for the steady state Navier-Stokes Darcy model discretized by mixed element methods. First, a Newton iterative method is introduced for solving the…
In this contribution, we are concerned with model order reduction in the context of iterative regularization methods for the solution of inverse problems arising from parameter identification in elliptic partial differential equations. Such…
In this era of large-scale data, distributed systems built on top of clusters of commodity hardware provide cheap and reliable storage and scalable processing of massive data. Here, we review recent work on developing and implementing…
This paper studies the finite-time stability and stabilization of linear discrete time-varying stochastic systems with multiplicative noise. Firstly, necessary and sufficient conditions for finite-time stability are presented via state…
This paper introduces a novel compact mixed integer linear programming (MILP) formulation and a discretization discovery-based solution approach for the Vehicle Routing Problem with Time Windows (VRPTW). We aim to solve the optimization…
In spite of its overall efficiency and robustness for capturing the interface in multiphase fluid dynamics simulations, the well-known shortcoming of the level-set method is associated with the lack of a systematic approach for preserving…
We improve the performance of multigrid solvers on many-core architectures with cache hierarchies by reorganizing operations in the smoothing step to minimize memory transfers. We focus on patch smoothers, which offer robust convergence…
Scaling up new scientific technologies from laboratory to industry often involves demonstrating performance on a larger scale. Computer simulations can accelerate design and predictions in the deployment process, though traditional…
A new time relaxation model with iterative modified Lavrentiev regularization method is studied. The aim of the relaxation term is to drive the unresolved fluctuations in a computational simulation to zero exponentially faster by an…
Hierarchical matrix approximations have gained significant traction in the machine learning and scientific community as they exploit available low-rank structures in kernel methods to compress the kernel matrix. The resulting compressed…
The use of implicit time-stepping schemes for the numerical approximation of solutions to stiff nonlinear time-evolution equations brings well-known advantages including, typically, better stability behaviour and corresponding support of…
In this paper we want to propose practical numerical methods to solve a class of initial-boundary problem of time-space fractional convection-diffusion equations (TSFCDEs). To start with, an implicit difference method based on two-sided…
We present a design and implementation of the Thomas algorithm optimized for hardware acceleration on an FPGA, the Thomas Core. The hardware-based algorithm combined with the custom data flow and low level parallelism available in an FPGA…
We propose a second-order temporally implicit, fourth-order-accurate spatial discretization scheme for the strongly anisotropic heat transport equation characteristic of hot, fusion-grade plasmas. Following [Du Toit et al., Comp. Phys.…
We propose an algorithm to compute the dynamics of articulated rigid-bodies with different sensor distributions. Prior to the on-line computations, the proposed algorithm performs an off-line optimisation step to simplify the computational…