Related papers: Towards Code Generation for Octree-Based Multigrid…
Kernel methods for solving partial differential equations on surfaces have the advantage that those methods work intrinsically on the surface and yield high approximation rates if the solution to the partial differential equation is smooth…
The implementation of efficient multigrid preconditioners for elliptic partial differential equations (PDEs) is a challenge due to the complexity of the resulting algorithms and corresponding computer code. For sophisticated finite element…
In this manuscript, we present a collective multigrid algorithm to solve efficiently the large saddle-point systems of equations that typically arise in PDE-constrained optimization under uncertainty, and develop a novel convergence…
Growing heterogeneity and configurability in HPC architectures has made auto-tuning applications and runtime parameters on these systems very complex. Users are presented with a multitude of options to configure parameters. In addition to…
In this paper we design a neural interpolation operator to improve the boundary data for regional weather models, which is a challenging problem as we are required to map multi-scale dynamics between grid resolutions. In particular, we…
Handling the ever-increasing complexity of mesh generation codes along with the intricacies of newer hardware often results in codes that are both difficult to comprehend and maintain. Different facets of codes such as thread management and…
We propose a sparse interpolation construction and a practical coarsening algorithm for the algebraic multigrid (AMG) method, tailored towards H(curl). Building on the generalized AMG framework, we introduce an interior/exterior splitting…
One of the primary areas of interest in High Performance Computing is the improvement of performance of parallel workloads. Nowadays, compilable source code-based optimization tasks that employ deep learning often exploit LLVM Intermediate…
Multigrid methods despite being known to be asymptotically optimal algorithms, depend on the careful selection of their individual components for efficiency. Also, they are mostly restricted to standard cycle types like V-, F-, and…
A simple and efficient interface-fitted mesh generation algorithm is developed in this paper. This algorithm can produce a local anisotropic fitting mixed mesh which consists of both triangles and quadrilaterals near the interface. A new…
The accurate assembly of the system matrix is an important step in any code that solves partial differential equations on a mesh. We either explicitly set up a matrix, or we work in a matrix-free environment where we have to be able to…
A surge in artificial intelligence and autonomous technologies have increased the demand toward enhanced edge-processing capabilities. Computational complexity and size of state-of-the-art Deep Neural Networks (DNNs) are rising…
We introduce a soft computing approach for automatically selecting and combining indices from remote sensing multispectral images that can be used for classification tasks. The proposed approach is based on a Genetic-Programming (GP)…
We present a deep learning-based iterative approach to solve the discrete heterogeneous Helmholtz equation for high wavenumbers. Combining classical iterative multigrid solvers and convolutional neural networks (CNNs) via preconditioning,…
We present a new high-level synthesis methodology for using large language model tools to generate hardware designs. The methodology uses exclusively open-source tools excluding the large language model. As a case study, we use our…
This paper presents an octree construction method, called Cornerstone, that facilitates global domain decomposition and interactions between particles in mesh-free numerical simulations. Our method is based on algorithms developed for 3D…
The problem of finding the solution of Partial Differential Equations (PDEs) plays a central role in modeling real world problems. Over the past years, Multigrid solvers have showed their robustness over other techniques, due to its high…
The goal of this primer is to provide a relatively short exposition of the basics of multigrid methods, simplified by focusing on fundamental concepts in a variational setting. This is done by way of a quadratic energy minimization…
Domain-specific languages (DSLs) play an increasingly important role in the generation of high performing software. They allow the user to exploit specific knowledge encoded in the constructs for the generation of code adapted to a…
Topology Optimization seeks to find the best design that satisfies a set of constraints while maximizing system performance. Traditional iterative optimization methods like SIMP can be computationally expensive and get stuck in local…