Questions tagged [discretization]

The process of representing a continuum space with a finite set of points/elements

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Why does the naive barycentric hodgestar fail?

The discrete exterior calculus is defined first using circumcentric dual cells, because the primal and dual edges are orthogonal and thus the dual cells are convex. This leads to a diagonal hodge star ...
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Order of accuracy of FVM discretization

I've recently got interested in CFD and started a small project by solving the radial Reynoldsequation. Why the Reynoldsequation? I recently encountered it through my studies and somehow got stuck :) ...
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How to account for the interface between two different phases in a discretized diffusion model?

I have tried to set up a model for the diffusion of a gas into a liquid. The two media are next to each other and the geometry is spherical because the system should simulate the diffusion out of a ...
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Lax equivalence theorem for integro-differential equation

Can the Lax equivalence theorem (http://en.wikipedia.org/wiki/Lax_equivalence_theorem) be applied to the discretization of integro-differential equations, or does a similar theorem exist for them?
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Which discretization scheme to use for elliptic PDE?

While simulating motion of nonlinear inelastic wire one meets the following equations \begin{align} &{\partial^2\varphi\over\partial t^2}=2{\partial F\over\partial s}{\partial\varphi\over\partial ...
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In sights into why higher order finite differencing method leads faster to instability

I was playing around with numerically solving the 1D wave equation with density and stiffness varying with position using central differencing methods and noticed that for certain discretization steps ...
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Literature on numerical solving based on multiple meshes?

Consider solving a differential equation system for 1D, 2D, or 3D. It involves various input and output "field" variables, which, more often than not, correspond to various physical quantities ...
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Time discretization of wave equation

I am trying to model the seismic wave equation and have therefore been reading about discretization schemes and their stability. I recently came across an insightful paper on 'Galerkin FEM methods for ...
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Finite difference aproximation - Darcy law

I am solving following problem: Filtration of water can be described in bi-dimensional case by $$- \partial_x(K(x,y) \partial_x u ) - \partial_y (K(x,y) \partial_y u ) = 0,$$ where $u$ - water ...
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Can the standard multigrid performance be used for time-dependent PDEs?

Consider a time dependent pde(i.e u(x,t)).I know when only space-coarsening is used the standard multigrid performance can be applied but what if instead we use only time-coarsening?Can we apply the ...
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Second and Higher Order Order Corrector in Spectral Deferred Correction

I am trying to work out a second order or higher order correction for the method of Spectral deferred Correction (SDC). Specifically using as a corrector a second order or third order multi-step. In ...
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Does scaling factor affect discretization?

Suppose I want to solve the below equation numerically. $$\frac{dy}{dx}=y$$ I'd like to normalize the space discretization by choosing $$a\bar{x}=x$$ where I assume $\bar{x}$ is unity. Then the ...
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Stability in Discretization of 1D Stationary Boltzmann equation

I want to discretize and numerically solve the following PDE: $$v(k)\dfrac{\partial f}{\partial x} + E(x)\dfrac{\partial f}{\partial k} = S\{f\}$$ using finite volume (box ...
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Do collocated grid arrangements definitely result in the checkerboard effect?

I understand the checkerboard effect due to the use of collocated grid arrangements in FVM. However, I wanted to know whether this problem is definitely bound to effect the results? For instance, I ...
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problem with understanding the fluid boundary conditions of a 1D probelm

I am having problems understanding the boundary conditions of the problem described in this paper on researchgate Essentially the problem consists of a one dimensional fluid chamber in contact with a ...
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Equilateral triangle based mesh generation by intersection

In work I am currently working on I need to mesh some structure with equilateral triangles to study it using a kind of discrete element method known as spring networks or Lattice model. To mesh the ...
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I am looking for help in the FE discretisation of the Laplace eigenkproblem with Neumann boundary conditions; that is, $$-\int_{\Omega} \nabla u \cdot \nabla v= \lambda \int_{\Omega} uv,$$ or $$Ax=\... 0answers 30 views Gridline cutouts after FFT and iFFT on Python EDIT: I think I messed up on the coordinates of (p,q). Num was missing a multiple of 2\pi/N. Assuming my interpretation of DFT isn't wrong. I am currently using FFT to run Fresnel Diffraction as ... 0answers 55 views Discretizing Multi-species Ion Exchange Equations by Finite Volume Method I'm solving a system of multispecies ion exchange equations (diffusion+drift fluxes) in 1-d spherical domain using finite volume method to obtain the ion concentrations at the next time step. After ... 1answer 80 views What is the rationale of second-order finite volume discretization? When it comes to a second-order accurate finite volume discretization of Navier-Stokes equations, which one of the two following rationales is adopted? 1- Second-order accuracy is a direct consequence ... 0answers 44 views How to solve for underlying function from discrete data set containing integral of that function New to Computational Science, I hope I'm on the right exchange network for this question. I have a time series data set that contains the sum of a source data set representing an exponential decay ... 0answers 68 views The relation between PDE order and discretization order In Jasak's Ph.D. thesis (2000), a notion is given about discretization of a transport equation: For good accuracy, it is necessary for the order of the discretization to be equal to or higher than the ... 0answers 79 views Analytic vs discrete understanding of PDE The PDE I am working with:$$\partial_tu = \nabla \cdot (a(x)\nabla u)-\beta(x)u\\ \partial_nu=0, x \in \Omega \subset \mathbb{R}^2\\ \beta(x)>0$$Integrate the PDE:$$\int_\Omega \partial_t u=\...
I'm discretizing the following Poisson equation using FVM where the domain $\Omega$ of the solution is a regular hexagon of side $1$ centered about the origin. \Delta u =k,\text{ $k$ constant}\\ \...