Related papers: A robust solver for large-scale heat transfer topo…
We introduce a neural-preconditioned iterative solver for Poisson equations with mixed boundary conditions. Typical Poisson discretizations yield large, ill-conditioned linear systems. Iterative solvers can be effective for these problems,…
Memory bound applications such as solvers for large sparse systems of equations remain a challenge for GPUs. Fast solvers should be based on numerically efficient algorithms and implemented such that global memory access is minimised. To…
The Poisson pressure solve resulting from the spectral element discretization of the incompressible Navier-Stokes equation requires fast, robust, and scalable preconditioning. In the current work, a parallel scaling study of…
This paper presents a multiscale methodology for efficient unsteady conjugate heat transfer simulations. The solid domain is modelled by coupling a global representation of the temperature field, based on the eigenfunctions of the unsteady…
This paper expands on the TRANSP description given in Computer Physics Communications 312 (2025) 109611 by describing recent progress in TRANSP's predictive functionality and emphasizing the development of the PT_SOLVER module and…
We consider the parallel-in-time solution of hyperbolic partial differential equation (PDE) systems in one spatial dimension, both linear and nonlinear. In the nonlinear setting, the discretized equations are solved with a preconditioned…
Solving optimization problems with transient PDE-constraints is computationally costly due to the number of nonlinear iterations and the cost of solving large-scale KKT matrices. These matrices scale with the size of the spatial…
Efficiently solving large-scale linear systems is a critical challenge in electromagnetic simulations, particularly when using the Crank-Nicolson Finite-Difference Time-Domain (CN-FDTD) method. Existing iterative solvers are commonly…
This paper presents our work on designing scalable linear solvers for large-scale reservoir simulations. The main objective is to support implementation of parallel reservoir simulators on distributed-memory parallel systems, where MPI…
Elliptic partial differential equations must be solved numerically for many problems in numerical relativity, such as initial data for every simulation of merging black holes and neutron stars. Existing elliptic solvers can take multiple…
Discrete variational methods show excellent performance in numerical simulations of different mechanical systems. In this paper, we introduce an iterative procedure for the solution of discrete variational equations for boundary value…
When integrating the radiative transfer equation for polarized light, the necessity of high-order numerical methods is well known. In fact, well-performing high-order formal solvers enable higher accuracy and the use of coarser spatial…
Coupled nonlinear system of reaction-diffusion equations describing multi-component (species) interactions with heterogeneous coefficients is considered. Finite volume method based approximation for the space is used to construct…
The construction of robust solvers for linear systems obtained from the discretization of partial differential equations using Isogeometric Analysis is challenging since the condition number of the system matrix not only grows with the…
We introduce CaLES, a GPU-accelerated finite-difference solver designed for large-eddy simulations (LES) of incompressible wall-bounded flows in massively parallel environments. Built upon the existing direct numerical simulation (DNS)…
Deep learning has emerged as a transformative tool for the neural surrogate modeling of partial differential equations (PDEs), known as neural PDE solvers. However, scaling these solvers to industrial-scale geometries with over $10^8$ cells…
A parallelization of a sweeping preconditioner for 3D Helmholtz equations without large cavities is introduced and benchmarked for several challenging velocity models. The setup and application costs of the sequential preconditioner are…
The focus of my PhD thesis is on exploring parallel approaches to efficiently solve problems modeled by constraints and presenting a new proposal. Current solvers are very advanced; they are carefully designed to effectively manage the…
Within high-performance computing (HPC), solving large sparse linear systems efficiently remains paramount, with iterative methods being the predominant choice. However, the performance of these methods is tightly coupled to the aptness of…
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…