Related papers: Quantum Element Method for Simulation of Quantum E…
We propose a framework to solve non-linear and history-dependent mechanical problems based on a hybrid classical computer -- quantum annealer approach. Quantum Computers are anticipated to solve particular operations exponentially faster.…
This work investigates a two-stage method for constructing projection-based reduced-order models (ROMs) of parameterized partial differential equations (PDEs). Based on established tensorial ROM methodology, the proposed approach reduces…
Chaotic free surface flows are challenging problems to simulate numerically, mainly due to the significant changes in geometry and frequent topological changes. Methods that track the evolution of the fluid in a Lagrangian formulation are a…
We present a quantum computing formulation to address a challenging problem in the development of probabilistic learning on manifolds (PLoM). It involves solving the spectral problem of the high-dimensional Fokker-Planck (FKP) operator,…
In the study of micro-swimmers, both artificial and biological ones, many-query problems arise naturally. Even with the use of advanced high performance computing (HPC), it is not possible to solve this kind of problems in an acceptable…
Fine-grained spectral properties of quantum Hamiltonians, including both eigenvalues and their multiplicities, provide useful information for characterizing many-body quantum systems as well as for understanding phenomena such as…
We are interested in the numerical solution of coupled nonlinear partial differential equations (PDEs) in two and three dimensions. Under certain assumptions on the domain, we take advantage of the Kronecker structure arising in standard…
Partial differential equations (PDEs) are crucial for modeling various physical phenomena such as heat transfer, fluid flow, and electromagnetic waves. In computer-aided engineering (CAE), the ability to handle fine resolutions and large…
We develop a geometrically intrinsic formulation of the arbitrary-order Virtual Element Method (VEM) on polygonal cells for the numerical solution of elliptic surface partial differential equations (PDEs). The PDE is first written in…
Reduced order modeling (ROM) is a field of techniques that approximates complex physics-based models of real-world processes by inexpensive surrogates that capture important dynamical characteristics with a smaller number of degrees of…
The finite element methods (FEM) are important techniques in engineering for solving partial differential equations, but they depend heavily on element shape quality for stability and good performance. In this paper, we introduce the…
Partial differential equations (PDEs) are fundamental across numerous scientific fields. As these problems scale to high dimensions, classical numerical schemes introduce severe computational bottlenecks, known as the curse of…
The Virtual Element Method (VEM) is a well-established framework for solving partial differential equations on polygonal and polyhedral meshes. In this paper, we introduce a novel hybrid VEM that integrates both conforming and nonconforming…
In this work we propose tailored model order reduction for varying boundary optimal control problems governed by parametric partial differential equations. With varying boundary control, we mean that a specific parameter changes where the…
Portfolio Optimization (PO) is a financial problem aiming to maximize the net gains while minimizing the risks in a given investment portfolio. The novelty of Quantum algorithms lies in their acclaimed potential and capability to solve…
In this paper we present algorithms for an efficient implementation of the Localized Orthogonal Decomposition method (LOD). The LOD is a multiscale method for the numerical simulation of partial differential equations with a continuum of…
The EMI (Extracellular-Membrane-Intracellular) model describes electrical activity in excitable tissue, where the extracellular and intracellular spaces and cellular membrane are explicitly represented. The model couples a system of partial…
Quantum subspace diagonalization (QSD) methods are quantum-classical hybrid methods, commonly used to find ground and excited state energies by projecting the Hamiltonian to a smaller subspace. In applying these, the choice of subspace…
Finite difference method and pseudo-spectral method have been widely used in the numerical relativity to solve the Einstein equations. As the third major category method to solve partial differential equations, finite element method is much…
Quantum simulators were originally proposed for simulating one partial differential equation (PDE) in particular - Schrodinger's equation. Can quantum simulators also efficiently simulate other PDEs? While most computational methods for…