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Quasi-Monte Carlo (QMC) methods are applied to multi-level Finite Element (FE) discretizations of elliptic partial differential equations (PDEs) with a random coefficient, to estimate expected values of linear functionals of the solution.…
Inverse uncertainty quantification (UQ) tasks such as parameter estimation are computationally demanding whenever dealing with physics-based models, and typically require repeated evaluations of complex numerical solvers. When partial…
Standard Model determinations of properties of strongly interacting systems of hadrons have become possible with the powerful method of lattice quantum chromodynamics (LQCD), a method with growing applicability and reliability. While growth…
Immersed boundary methods are high-order accurate computational tools used to model geometrically complex problems in computational mechanics. While traditional finite element methods require the construction of high-quality boundary-fitted…
In this paper, we construct a combined multiscale finite element method (MsFEM) using the Local Orthogonal Decomposition (LOD) technique to solve the multiscale problems which may have singularities in some special portions of the…
Finite differences, finite elements, and their generalizations are widely used for solving partial differential equations, and their high-order variants have respective advantages and disadvantages. Traditionally, these methods are treated…
Immersed finite element methods provide a convenient analysis framework for problems involving geometrically complex domains, such as those found in topology optimization and microstructures for engineered materials. However, their…
Quantum chromodynamics (QCD) at non-zero isospin chemical potential is studied in a canonical approach by analyzing systems of fixed isospin number density. To construct these systems, we develop a range of new algorithms for performing the…
In our recent work [1] on lattice QCD calculation of the baryon leading-twist LCDAs within the framework of LaMET, a novel hybrid renormalization scheme is implemented for octet baryon quasi-DAs, yielding reliable results across both…
When modelling discontinuities (interfaces) using the finite element method, the standard approach is to use a conforming finite-element mesh in which the mesh matches the interfaces. However, this approach can prove cumbersome if the…
We study the phase structure of QCD at finite temperature and density by numerical simulations on a lattice. The most important point for the numerical study at finite density is treatment of the sign problem. We propose a method to avoid…
The combination of nonlinear FETI-DP (Dual Primal Finite Element Tearing and Interconnecting) and Quasi-Newton methods using a sequential quadratic programming (SQP) approach is considered. Nonlinear FETI-DP methods are parallel iterative…
The pseudopotential model within the Lattice Boltzmann Method (LBM) framework has emerged as a prominent approach in computational fluid dynamics due to its dual strengths in physical intuitiveness and computational tractability. However,…
In this work, we present the first implementation of the face-centered cubic (FCC) lattice model for protein structure prediction with a quantum algorithm. Our motivation to encode the FCC lattice stems from our observation that the FCC…
Natural cellular materials, such as honeycombs, woods, foams, trabecular bones, plant parenchyma, and sponges, may benefit from the disorderliness within their internal microstructures to achieve damage tolerant behaviours. Inspired by…
Precision tests of QCD perturbation theory are not readily available from experimental data. The main reasons are systematic uncertainties due to the confinement of quarks and gluons, as well as kinematical constraints which limit the…
We simulate lattice QCD at finite quark-number chemical potential to study nuclear matter, using the complex Langevin equation (CLE). The CLE is used because the fermion determinant is complex so that standard methods relying on importance…
The surge of activity in the resolution of fine scale features in the field of earth sciences over the past decade necessitates the development of robust yet simple algorithms that can tackle the various drawbacks of in silico models…
We introduce generalised finite difference methods for solving fully nonlinear elliptic partial differential equations. Methods are based on piecewise Cartesian meshes augmented by additional points along the boundary. This allows for…
The quasi-independent curvilinear coordinate approximation (QUICCA) method [K. N\'emeth and M. Challacombe, J. Chem. Phys. {\bf 121}, 2877, (2004)] is extended to the optimization of crystal structures. We demonstrate that QUICCA is valid…