We apply the tensor train (TT) decomposition to construct the tensor product polynomial
chaos expansion (PCE) of a random field, to solve the stochastic elliptic diffusion PDE with …

We resume the recent successes of the grid-based tensor numerical methods and discuss
their prospects in real-space electronic structure calculations. These methods, based on the …

We present a brief survey on the modern tensor numerical methods for multidimensional
stationary and time-dependent partial differential equations (PDEs). The guiding principle of …

We present a framework using the Quantized Tensor Train (qtt) decomposition to accurately
and efficiently solve volume and boundary integral equations in three dimensions. We …

Folding grid value vectors of size 2^ L 2 L into L th-order tensors of mode size 2 * ⋯ * 2 2×⋯×
2, combined with low-rank representation in the tensor train format, has been shown to result …

Our recent method for low-rank tensor representation of sums of the arbitrarily positioned
electrostatic potentials discretized on a 3D Cartesian grid reduces the 3D tensor summation …

Background: The computational resources needed to generate the ab initio solution of the
nuclear many-body problem for increasing mass number and/or accuracy necessitates …

In this paper, we propose and study two approaches to approximate the solution of the
Bethe–Salpeter equation (BSE) by using structured iterative eigenvalue solvers. Both …

We describe an efficient projection-based real-space implementation of the nonlocal single-
determinant exchange operator. Through a matrix representation of the projected operator …

We introduce and analyze the new range-separated (RS) canonical/Tucker tensor format
which aims for numerical modeling of the 3D long-range interaction potentials in …