Related papers: Towards Neural Sparse Linear Solvers
Integrating renewable resources within the transmission grid at a wide scale poses significant challenges for economic dispatch as it requires analysis with more optimization parameters, constraints, and sources of uncertainty. This…
The solution of large sparse linear systems is often the most time-consuming part of many science and engineering applications. Computational fluid dynamics, circuit simulation, power network analysis, and material science are just a few…
Nowadays, several industrial applications are being ported to parallel architectures. In fact, these platforms allow acquire more performance for system modelling and simulation. In the electric machines area, there are many problems which…
Efficient solutions of large-scale, ill-conditioned and indefinite algebraic equations are ubiquitously needed in numerous computational fields, including multiphysics simulations, machine learning, and data science. Because of their…
This survey describes a class of methods known as "fast direct solvers". These algorithms address the problem of solving a system of linear equations $\boldsymbol{Ax}=\boldsymbol{b}$ arising from the discretization of either an elliptic PDE…
The linear equations that arise in interior methods for constrained optimization are sparse symmetric indefinite and become extremely ill-conditioned as the interior method converges. These linear systems present a challenge for existing…
Inversion of sparse matrices with standard direct solve schemes is robust, but computationally expensive. Iterative solvers, on the other hand, demonstrate better scalability; but, need to be used with an appropriate preconditioner (e.g.,…
We describe the GPU implementation of shifted or multimass iterative solvers for sparse linear systems of the sort encountered in lattice gauge theory. We provide a generic tool that can be used by those without GPU programming experience…
Solving sparse linear systems from discretized PDEs is challenging. Direct solvers have in many cases quadratic complexity (depending on geometry), while iterative solvers require problem dependent preconditioners to be robust and…
We discuss an approach for solving sparse or dense banded linear systems ${\bf A} {\bf x} = {\bf b}$ on a Graphics Processing Unit (GPU) card. The matrix ${\bf A} \in {\mathbb{R}}^{N \times N}$ is possibly nonsymmetric and moderately large;…
Linear solvers are major computational bottlenecks in a wide range of decision support and optimization computations. The challenges become even more pronounced on heterogeneous hardware, where traditional sparse numerical linear algebra…
Sparse linear system solvers ($Ax=b$) are critical computational kernels in Electronic Design Automation (EDA), underpinning vital simulations for modern IC and system design. Applications like power integrity verification and…
This paper proposes a new distributed algorithm for solving linear systems associated with a sparse graph under a generalised diagonal dominance assumption. The algorithm runs iteratively on each node of the graph, with low complexities on…
Machine learning is increasingly used to improve decisions within branch-and-bound algorithms for mixed-integer programming. Many existing approaches rely on deep learning, which often requires very large training datasets and substantial…
Recently, graphics processors (GPUs) have been increasingly leveraged in a variety of scientific computing applications. However, architectural differences between CPUs and GPUs necessitate the development of algorithms that take advantage…
Large sparse linear algebraic systems can be found in a variety of scientific and engineering fields, and many scientists strive to solve them in an efficient and robust manner. In this paper, we propose an interpretable neural solver, the…
Efficient numerical solvers for sparse linear systems are crucial in science and engineering. One of the fastest methods for solving large-scale sparse linear systems is algebraic multigrid (AMG). The main challenge in the construction of…
Iterative solutions of sparse linear systems and sparse eigenvalue problems have a fundamental role in vital fields of scientific research and engineering. The crucial computing kernel for such iterative solutions is the multiplication of a…
A brief summary of direct solution approaches for finite element methods (FEM) in computational electromagnetics (CEM) is given along with an alternative direct solution based on domain decomposition (DD). Unlike recent trends in…
The parallel linear equations solver capable of effectively using 1000+ processors becomes the bottleneck of large-scale implicit engineering simulations. In this paper, we present a new hierarchical parallel master-slave-structural…