相关论文: Multithreaded Filtering Preconditioner for Diffusi…
In this paper, we design an algorithm to accelerate the diffusion process on the $SO(3)$ manifold. The inherently sequential nature of diffusion models necessitates substantial time for denoising perturbed data. To overcome this limitation,…
Although some preconditioners are available for solving dense linear systems, there are still many matrices for which preconditioners are lacking, in particular in cases where the size of the matrix $N$ becomes very large. There remains…
We develop a parallel-in-time multigrid preconditioner for augmented systems. These saddle-point systems are foundational to numerical optimization. Our preconditioner, when paired with a suitable optimization method, accelerates the…
In this paper, we develop a multigrid preconditioner to solve Darcy flow in highly heterogeneous porous media. The key component of the preconditioner is to construct a sequence of nested subspaces $W_{\mathcal{L}}\subset…
In this paper, we study fast iterative solvers for the solution of fourth order parabolic equations discretized by mixed finite element methods. We propose to use consistent mass matrix in the discretization and use lumped mass matrix to…
We introduce a neural-preconditioned iterative solver for Poisson equations with mixed boundary conditions. Typical Poisson discretizations yield large, ill-conditioned linear systems. Iterative solvers can be effective for these problems,…
Diffusion transformers have gained substantial interest in diffusion generative modeling due to their outstanding performance. However, their computational demands, particularly the quadratic complexity of attention mechanisms and…
Sparse linear system solvers are computationally expensive kernels that lie at the heart of numerous applications. This paper proposes a flexible preconditioning framework to substantially reduce the time and energy requirements of this…
To analyze large sets of grid states, e.g. when evaluating the impact from the uncertainties of the renewable generation with probabilistic Monte Carlo simulation or in stationary time series simulation, large number of power flow…
Pore-scale simulations accurately describe transport properties of fluids in the subsurface. These simulations enhance our understanding of applications such as assessing hydrogen storage efficiency and forecasting CO$_2$ sequestration…
The multigroup neutron transport criticality calculations using modern supercomputers have been widely employed in a nuclear reactor analysis for studying whether or not a system is self-sustaining. However, the design and development of…
Diffusion models have proven to be highly effective in generating high-quality images. However, adapting large pre-trained diffusion models to new domains remains an open challenge, which is critical for real-world applications. This paper…
We present a robust and scalable preconditioner for the solution of large-scale linear systems that arise from the discretization of elliptic PDEs amenable to rank compression. The preconditioner is based on hierarchical low-rank…
The boundary integral method is an efficient approach for solving time-harmonic obstacle scattering problems by a bounded scatterer. This paper presents the directional preconditioner for the iterative solution of linear systems of the…
Large-scale parallel numerical simulations are essential for a wide range of engineering problems that involve complex, coupled physical processes interacting across a broad range of spatial and temporal scales. The data structures involved…
Numerical solution of reaction-diffusion equations in three dimensions is one of the most challenging applied mathematical problems. Since these simulations are very time consuming, any ideas and strategies aiming at the reduction of CPU…
We introduce a class of efficient multiple right-hand side multigrid algorithm for domain wall fermions. The simultaneous solution for a modest number of right hand sides concurrently allows for a significant reduction in the time spent…
Upcoming many core processors are expected to employ a distributed memory architecture similar to currently available supercomputers, but parallel pattern mining algorithms amenable to the architecture are not comprehensively studied. We…
Bundle adjustment is an important global optimization step in many structure from motion pipelines. Performance is dependent on the speed of the linear solver used to compute steps towards the optimum. For large problems, the current state…
Purpose: Design of a preconditioner for fast and efficient parallel imaging and compressed sensing reconstructions. Theory: Parallel imaging and compressed sensing reconstructions become time consuming when the problem size or the number of…