6 papers · 1 filter
Completely Positive and Trace Preserving Schemes with Tensor Train Compression for the Lindblad Equation
Peter DelMastro, Daniel Appelö, Yingda Cheng
We propose a family of low-rank, completely positive and trace preserving schemes for the Lindblad equation, a common model for open quantum systems. Low-rank representation is emp…
Arbitrary High Order Low-rank Completely Positive and Trace Preserving (CPTP) Schemes for Lindblad Equations with Time-dependent Hamiltonian
Jiuhua Hu, Daniel Appelo, Yingda Cheng
In this paper, we develop a framework for designing arbitrary high order low-rank schemes for the Lindblad equation with time-dependent Hamiltonians. Our approach is based on neste…
A new cross approximation for Tucker tensors and its application in Tucker-Anderson Acceleration
Daniel Appelö, Yingda Cheng
This paper proposes two new algorithms related to the Tucker tensor format. The first method is a new cross approximation for Tucker tensors, which we call Cross-DEIM. Cross$^2…
lrAA: Low-Rank Anderson Acceleration
Daniel Appelo, Yingda Cheng
This paper proposes a new framework for computing low-rank solutions to nonlinear matrix equations arising from spatial discretization of nonlinear partial differential equations:…
High-Order Implicit Low-Rank Method with Spectral Deferred Correction for Matrix Differential Equations
Shun Li, Yan Jiang, Yingda Cheng
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 lo…
Preconditioning Low Rank Generalized Minimal Residual Method (GMRES) for Implicit Discretizations of Matrix Differential Equations
Shixu Meng, Daniel Appelo, Yingda Cheng
This work proposes a new class of preconditioners for the low rank Generalized Minimal Residual Method (GMRES) for multiterm matrix equations arising from implicit timestepping of…