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On detecting a wavefront described by a 2D eikonal equation when the velocity in the medium depends on one spatial variable
Pleiades Publishing Ltd - Tập 3 - Trang 52-58 - 2010
In this paper, the 2D eikonal equation f 2 + f 2 = (ky + b)2α is considered. If
a solution is found, the relation f (x, y) = C determines the location of the
wavefront. However, finding the solutions is still an open question. In this
paper, we propose to directly find a curve in parametric form, which determines
the wavefront without solving the equation....
The lagrange multiplier method for solving a semicoercive model problem with friction
Pleiades Publishing Ltd - Tập 2 - Trang 330-340 - 2009
In model problems with friction, unconditional minimization of a
nondifferentiable functional is reduced to conditional minimization of a
differentiable functional. To solve the semicoercive problem obtained, we use a
dual scheme based on a modified Lagrangian functional.
Difference Methods for Solving Nonlocal Boundary Value Problems for Fractional-Order Pseudo-Parabolic Equations with the Bessel Operator
Pleiades Publishing Ltd - - 2020
Reverse-time continuation of elastic waves
Pleiades Publishing Ltd - Tập 2 - Trang 272-280 - 2009
Methods based on downward continuation of an oscillation field have received
wide recognition in the processing of multichannel seismic prospecting data.
Physically, the idea behind this approach is clear: a wavefield observed on some
surface is continued into the medium and backward in time. Mathematically, all
the continuation algorithms used are based on scalar wave equation modeling,
which tak...
L ∞-error estimates of triangular mixed finite element methods for optimal control problems governed by semilinear elliptic equations
Pleiades Publishing Ltd - - 2009
Theoretical justification of interior point algorithms for solving optimization problems with nonlinear constraints
Pleiades Publishing Ltd - Tập 6 - Trang 24-33 - 2013
A family of interior point algorithms is considered. These algorithms can be
used for solving mathematical programming problems with nonlinear inequality
constraints. Some weighted Euclidean norms are applied to finding a descent
direction for improving the solution. These norms vary with iterations. A
theoretical justification of the algorithms with some assumptions (including the
nonsingularity ...
A problem with wells for the steady diffusion equation
Pleiades Publishing Ltd - Tập 3 - Trang 101-117 - 2010
This paper deals with a problem with wells for which nonlocal boundary
conditions are given. It is shown that the problem is equivalent to a mixed
problem without wells. For this formulation, an error estimate of a mixed finite
element method in the 2D case is studied.
Estimation of Pointwise Approximation Error Using a Set of Numerical Solutions
Pleiades Publishing Ltd - Tập 15 - Trang 281-292 - 2022
This paper deals with estimation of local (pointwise) approximation error on an
ensemble of numerical solutions obtained by using independent algorithms. A
variational inverse problem is posed for approximation error estimation. This
problem is ill-posed due to translation-invariance of the governing equations.
Zero order Tikhonov regularization is applied to obtain stable solutions.
Numerical tes...
Parallel algorithms and domain decomposition techniques for solving three-dimensional boundary value problems on quasi-structured grids
Pleiades Publishing Ltd - Tập 9 - Trang 141-149 - 2016
A new approach to the decomposition of a three-dimensional computational domain
into subdomains matched without overlapping is proposed. It is based on direct
approximation of the Poincare–Steklov equation at the interface. Parallel
algorithms and techniques for solving threedimensional boundary value problems
on quasi-structured grids are presented. Experimental evaluation of parallel
efficiency ...
Mathematical Modeling of a Positive Connection in the p53-microRNA Tumor Marker System
Pleiades Publishing Ltd - Tập 12 - Trang 270-283 - 2019
A hierarchy of minimal mathematical models of the dynamics of the p53-Mdm2-
microRNA system has been developed. The models are based on differential
equations with a time delay, describing complex interaction mechanisms in the
signal system of the p53 protein. We consider two types of interaction of p53
with microRNAs: a positive direct connection and a positive feedback. The
feedback of microRNA-...
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