Related papers: pySDC - Prototyping spectral deferred corrections
Stochastic gradient descent (SGD) algorithm and its variations have been effectively used to optimize neural network models. However, with the rapid growth of big data and deep learning, SGD is no longer the most suitable choice due to its…
Spatially coupled, parallel concatenated codes (SC-PCCs) have been shown to approach channel capacity when decoded using optimal iterative methods. However, under complexity constraints such decoding strategies can result in unacceptable…
In this work we analyze the convergence properties of the Spectral Deferred Correction (SDC) method originally proposed by Dutt et al. [BIT, 40 (2000), pp. 241--266]. The framework for this high-order ordinary differential equation (ODE)…
In this paper, we develop a low-rank method with high-order temporal accuracy using spectral deferred correction (SDC) to compute linear matrix differential equations. In [1], a low rank numerical method is proposed to correct the modeling…
HDSDP is a numerical software solving the semidefinite programming problems. The main framework of HDSDP resembles the dual-scaling interior point solver DSDP [BY2008] and several new features, including a dual method based on the…
A class of nonstandard pseudospectral time domain (PSTD) schemes for solving time-dependent hyperbolic and parabolic partial differential equations (PDEs) is introduced. These schemes use the Fourier collocation spectral method to compute…
Adaptive stepsize control is a critical feature for the robust and efficient numerical solution of initial-value problems in ordinary differential equations. In this paper, we show that adaptive stepsize control can be incorporated within a…
We propose SparseDC, a model for Depth Completion of Sparse and non-uniform depth inputs. Unlike previous methods focusing on completing fixed distributions on benchmark datasets (e.g., NYU with 500 points, KITTI with 64 lines), SparseDC is…
The paper investigates two new use cases for the Boris Spectral Deferred Corrections (Boris-SDC) time integrator for plasma simulations. First, we show that using Boris-SDC as a particle pusher in an electrostatic particle-in-cell (PIC)…
Semidefinite programming (SDP) provides a principled framework for convex relaxations of nonconvex geometric constraints in motion planning, yet existing solvers are too computationally expensive for real-time control, particularly on…
Time-parallel time integration has received a lot of attention in the high performance computing community over the past two decades. Indeed, it has been shown that parallel-in-time techniques have the potential to remedy one of the main…
Integrated localization and communication systems aim to reuse communication waveforms for simultaneous data transmission and localization, but delay resolution is fundamentally limited by the available bandwidth. In practice, large…
A symplectic pseudospectral time-domain (SPSTD) scheme is developed to solve Schrodinger equation. Instead of spatial finite differences in conventional finite-difference time-domain (FDTD) method, the fast Fourier transform is used to…
We present a fourth-order finite-volume algorithm in space and time for low Mach number reacting flow with detailed kinetics and transport. Our temporal integration scheme is based on a multi-implicit spectral deferred correction (MISDC)…
PySDM is an open-source Python package for simulating the dynamics of particles undergoing condensational and collisional growth, interacting with a fluid flow and subject to chemical composition changes. It is intended to serve as a…
We present an arbitrarily high-order, conditionally stable, partitioned spectral deferred correction (SDC) method for solving multiphysics problems using a sequence of pre-existing single-physics solvers. This method extends the work in [1,…
We propose an efficient approach to semidefinite spectral clustering (SSC), which addresses the Frobenius normalization with the positive semidefinite (p.s.d.) constraint for spectral clustering. Compared with the original Frobenius norm…
We present an adaptive arbitrary-order accurate time-stepping numerical scheme for the flow of vesicles suspended in Stokesian fluids. Our scheme can be summarized as an approximate implicit spectral deferred correction (SDC) method.…
We present convergence results in expectation for stochastic subspace correction schemes and their accelerated versions to solve symmetric positive-definite variational problems, and discuss their potential for achieving fault tolerance in…
We construct a space-time parallel method for solving parabolic partial differential equations by coupling the Parareal algorithm in time with overlapping domain decomposition in space. The goal is to obtain a discretization consisting of…