Related papers: Convex Optimization-Based Structure-Preserving Fil…
The modeling of large deformation fracture mechanics has been a challenging problem regarding the accuracy of numerical methods and their ability to deal with considerable changes in deformations of meshes where having the presence of…
In this work, we employ the Constraint Energy Minimizing Generalized Multiscale Finite Element Method (CEM-GMsFEM) to solve the problem of linear heterogeneous poroelasticity with coefficients of high contrast. The proposed method makes use…
Optimization of frame structures is formulated as a~non-convex optimization problem, which is currently solved to local optimality. In this contribution, we investigate four optimization approaches: (i) general non-linear optimization, (ii)…
In this paper, we discuss the application of the Generalized Finite Element Method (GFEM) to approximate the solutions of quasilinear elliptic equations with multiple interfaces in one dimensional space. The problem is characterized by…
This paper is concerned with mixed finite element method (FEM) for solving the two-dimensional, nonlinear fourth-order active fluid equations. By introducing an auxiliary variable $w=-\Delta u$, the original fourth problem is transformed…
From a mathematical perspective, the extraordinary properties of metamaterials are often reflected in the coefficients of the governing partial differential equations (PDEs). These coefficients may fall outside the assumptions of classical…
Generalized or extended finite element methods (GFEM/XFEM) are in general badly conditioned and have numerous additional degrees of freedom (DOF) compared with the FEM because of introduction of enriched functions. In this paper, we develop…
In this paper, we generalize the chance optimization problems and introduce constrained volume optimization where enables us to obtain convex formulation for challenging problems in systems and control. We show that many different problems…
The Finite Element Method (FEM) is a powerful computational tool for solving partial differential equations (PDEs). Although commercial and open-source FEM software packages are widely available, an independent implementation of FEM…
With the increase in data availability, it has been widely demonstrated that neural networks (NN) can capture complex system dynamics precisely in a data-driven manner. However, the architectural complexity and nonlinearity of the NNs make…
In the present work we introduce a novel refinement algorithm for two-dimensional elliptic partial differential equations discretized with Virtual Element Method (VEM). The algorithm improves the numerical solution accuracy and the mesh…
By the simple finite element method, we study the symplectic, multisymplectic structures and relevant preserving properties in some semi-linear elliptic boundary value problem in one-dimensional and two-dimensional spaces respectively. We…
Achieving accurate numerical results of hydrodynamic loads based on the potential-flow theory is very challenging for structures with sharp edges, due to the singular behavior of the local-flow velocities. In this paper, we introduce the…
The virtual element method (VEM) is a stabilized Galerkin method that is robust and accurate on general polygonal meshes. This feature makes it an appealing candidate for simulations involving meshes with embedded interfaces and evolving…
Since the 1960's the finite element method emerged as a powerful tool for the numerical simulation of countless physical phenomena or processes in applied sciences. One of the reasons for this undeniable success is the great versatility of…
Numerical simulations of waves in highly heterogeneous media have important applications, but direct computations are prohibitively expensive. In this paper, we develop a new generalized multiscale finite element method with the aim of…
Reservoir simulators utilize numerical techniques to solve the governing equations of fluid flow in porous media and they are essential tool for oil and gas fields development. In practical reservoir simulation, the finite difference method…
We propose a general method for optimization with semi-infinite constraints that involve a linear combination of functions, focusing on the case of the exponential function. Each function is lower and upper bounded on sub-intervals by…
In fractured natural formations, the equations governing fluid flow and geomechanics are strongly coupled. Hydrodynamical properties depend on the mechanical configuration, and they are therefore difficult to accurately resolve using…
Simulating flow in a highly heterogeneous reservoir with multiscale characteristics could be considerably demanding. To tackle this problem, we propose a numerical scheme coupling the Generalized Multiscale Finite Element Method (GMsFEM)…