Related papers: Code generation for AMReX with applications to num…

PDE-to-solver code generation aims to automatically synthesize executable numerical solvers from partial differential equation (PDE) specifications. This task requires not only understanding the mathematical structure of PDEs, but also…

In this paper, a nonsmooth semilinear parabolic partial differential equation (PDE) is considered. For a reduced basis (RB) approach, a space-time formulation is used to develop a certified a-posteriori error estimator. This error estimator…

This work deals with partial MDS (PMDS) codes, a special class of locally repairable codes, used for distributed storage system. We first show that a known construction of these codes, using Gabidulin codes, can be extended to use any…

We have developed a gravity solver based on combining the well developed Particle-Mesh (PM) method and TREE methods. It is designed for and has been implemented on parallel computer architectures. The new code can deal with tens of millions…

Quantum random number generator harnesses the power of quantum mechanics to generate true random numbers, making it valuable for various scientific applications. However, real-world devices often suffer from imperfections that can undermine…

ExaGRyPE describes a suite of solvers for numerical relativity, based upon ExaHyPE 2, the second generation of our Exascale Hyperbolic PDE Engine. The presented generation of ExaGRyPE solves the Einstein equations in the CCZ4 formulation…

This paper introduces a novel research direction for model-to-text/code transformations by leveraging Large Language Models (LLMs) that can be enhanced with Retrieval-Augmented Generation (RAG) pipelines. The focus is on quantum and hybrid…

A general multi-terminal source code and a general multi-terminal channel code are presented. Constrained-random-number generators with sparse matrices, which are building blocks for the code construction, are used in the construction of…

In the past few years, Large Language Models (LLMs) have exploded in usefulness and popularity for code generation tasks. However, LLMs still struggle with accuracy and are unsuitable for high-risk applications without additional oversight…

A hierarchy of semidefinite programming (SDP) relaxations approximates the global optimum of polynomial optimization problems of noncommuting variables. Generating the relaxation, however, is a computationally demanding task, and only…

In this work, we introduce GRChombo: a new numerical relativity code which incorporates full adaptive mesh refinement (AMR) using block structured Berger-Rigoutsos grid generation. The code supports non-trivial "many-boxes-in-many-boxes"…

We describe the newly written code GADGET which is suitable both for cosmological simulations of structure formation and for the simulation of interacting galaxies. GADGET evolves self-gravitating collisionless fluids with the traditional…

In this paper, we examine algebraic geometric (AG) codes associated with curves generated by separated polynomials, and we create AG codes and quantum stabilizer codes from these curves by varying their parameters. Our research involves a…

Code transformation is a foundational capability in the software development process, where its effectiveness relies on constructing a high-quality code representation to characterize the input code semantics and guide the transformation.…

A family of high rate quantum error correcting codes adapted to the amplitude damping channel is presented. These codes are nonadditive and exploit self-complementarity structure to correct all first-order errors. Their rates can be higher…

We present IrRep - a Python code that calculates the symmetry eigenvalues of electronic Bloch states in crystalline solids and the irreducible representations under which they transform. As input it receives bandstructures computed with…

As an entry for the 2001 Gordon Bell Award in the "special" category, we describe our 3-d, hybrid, adaptive mesh refinement (AMR) code, Enzo, designed for high-resolution, multiphysics, cosmological structure formation simulations. Our…

The objective of this paper is to design an efficient and convergent alternating direction method of multipliers (ADMM) for finding a solution of medium accuracy to conic programming problems whose constraints consist of linear equalities,…

Semidefinite relaxations are widely used to compute upper bounds on the objective of optimization problems involving noncommutative polynomials. Such optimization problems are prevalent in quantum information. We present an algorithm able…

The applications of numerical relativity to cosmology are on the rise, contributing insight into such cosmological problems as structure formation, primordial phase transitions, gravitational-wave generation, and inflation. In this paper, I…