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Universal AMG Accelerated Embedded Boundary Method Without Small Cell Stiffness
We develop a universally applicable embedded boundary finite difference method, which results in a symmetric positive definite linear system and does...
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Self-Similar Solution of the Problem of Superheated Water Vapor Injection into a Porous Reservoir
AbstractBased on the mechanics of multiphase media methods and equations, a mathematical model of superheated water vapor injection into a reservoir...
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A Fast Single-Pass Method for Solving the Generalized Eikonal Equation in a Moving Medium
AbstractWe develop a fast method for approximating the solution to the generalized eikonal equation in a moving medium. Our approach consists of the...
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Computing the Minimum-Time Interception of a Moving Target
In this study, we propose an algorithmic framework for solving a class of optimal control problems. This class is associated with the minimum-time...
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On Nonlinear Boundary Value Problems for Differential Inclusions
AbstractWe consider autonomous differential inclusions with nonlinear boundary conditions. Sufficient conditions for the existence of solutions in...
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Dynamic Response to Moving Distributed Masses of Prestressed Orthotropic Cantilever Plate Resting on Variable Pasternak Elastic Foundation
This work is investigated the dynamic behaviour under moving distributed masses of prestressed orthotropic cantilever plates resting on variable...
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Anisotropic Adaptation of Moving Unstructured Mesh to Bodies of Complex Shapes Described by an Interpolation Octree
AbstractA methodology for anisotropic adaptation of a moving unstructured mesh to the surface of an object of arbitrary shape with account for its...
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A shape design problem for the Navier–Stokes flow with a convective boundary condition
In this study, a shape optimization problem for the two-dimensional stationary Navier–Stokes equations with an artificial boundary condition is...
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Closed-form steady-state solutions for forced vibration of second-order axially moving systems
Second-order axially moving systems are common models in the field of dynamics, such as axially moving strings, cables, and belts. In the traditional...
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Exponential Time Differencing Method for a Reaction- Diffusion System with Free Boundary
For reaction-diffusion equations in irregular domains with moving boundaries, the numerical stability constraints from the reaction and diffusion...
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Asymptotic Behavior of Solutions for Multi-stable Equation with Dirichlet Boundary Condition
We study a free boundary problem with a type of multi-stable nonlinearity and a Dirichlet boundary condition, the model describes the spreading of...
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The Problem of Target Control for a Quadrotor When Moving in a Horizontal Plane Avoiding Obstacles
AbstractA solution is sought for the problem of control in a mathematical model of the quadrotor. The main aim is moving an autonomous air vehicle...
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Global existence and large-time behavior for primitive equations with the free boundary
In the present paper, the primitive equations, which can be used to simulate the large-scale motion of the ocean and atmosphere, are considered in...
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The Existence of Solutions for a Free Boundary Problem Modeling the Spread of Ecosystem Engineers
Most models for the spread of an invasive species into a new environment are based on Fisher’s reaction–diffusion equation. They assume that habitat...
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Numerical Solution of the Vibration Suppression Problem for a Moving Web
AbstractMechanical processes occurring in paper production are modeled. In a papermaking machine, paper moves in the form of a thin sheet. The...
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Convergence and computational cost analysis of a boundary integral method applied to a rigid body moving in a viscous fluid in close proximity to a fixed boundary
The Boundary Integral Method (BIM) applied to the unsteady Stokes and continuity equations is a standard method used to simulate problems of bodies...
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Fractional Stefan Problem: A Survey of the Recent Results
AbstractThe paper presents a survey of the recent fractional generalizations of the Stefan problem. This free boundary value problem in the classical...
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Generalized Riemann Problem on the Decay of a Discontinuity with Additional Conditions at the Boundary and Its Application for Constructing Computational Algorithms
We construct an approximation of the fundamental solution of a problem for a hyperbolic system of first-order linear differential equations with...
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The Gradient Descent Method for the Convexification to Solve Boundary Value Problems of Quasi-Linear PDEs and a Coefficient Inverse Problem
We study the global convergence of the gradient descent method of the minimization of strictly convex functionals on an open and bounded set of a...
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On Unstable Solutions with a Nonmonotone Boundary Layer in a Two-Dimensional Reaction-Diffusion Problem
AbstractThe paper deals with the study of time-periodic solutions of boundary layer type for a two-dimensional reaction-diffusion problem with a...
