All Questions
Tagged with finite-difference finite-element
64
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142
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"Cleanest, most professional" approach to implement a finite differences scheme in dimension greater than two
Coding a finite difference algorithm in 1D does not require a complex mesh. In higher dimensions, you would need a mesh and its connectivity graph to compute the differential operators. Finite ...
- 147
1
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1
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149
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Can domain decomposition methods also be applied to linear systems resulting from finite difference discretizations?
Question
In general, do domain decomposition methods (DDMs) require a linear system of equations $Au = f$ to be formed by finite element discretization/method (FEM) of a PDE? Or could one simply use a ...
- 265
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95
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Reference request: graph Laplacian approximation for domains/manifolds
Is there any reference on solving the heat equation on irregular geometries via creating a mesh and using the graph Laplacian instead of FEM techniques? (Convergence to real solution).
That is to say, ...
- 181
1
vote
1
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153
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how to solve a coupled nonlinear partial differential equations(Boundary Value Problem)
So far, I have been looking into linear and nonlinear differential equations(Boundary value problem) that look like the following:
$\frac{d^2 \theta}{dz^2} + \sin(\theta) = 0$
I am now familiar with ...
- 35
4
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1
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252
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ON the Kronecker product form of the laplacian matrix
It's well known that if we use 2nd order, centered, finite differences for the Laplace operator, we have that the matrix can be written as $$K=I \otimes A + A \otimes I $$ where $I$ is the identity ...
- 405
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78
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How can I correctly determine velocity of a point inside a grid after using mixed finite element method to solve Poisson equation?
I am using the mixed finite element method (MFEM) to solve the Poisson equation:
$$\Delta h = 0,$$where $h$ denotes hydraulic pressure. The MFEM could determine the normal flux rate, $q_n$, through ...
- 323
3
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164
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Numerical calculation of out-of-time order correlators (OTOCs)
I want to numerically calculate OTOCs for different quantum mechanical systems. Consider the following Hamiltonian
$$H=p_x^2+p_y^2+x^2y^2$$
and I want to calculate the following OTOC
$$C_T(t)=-\left&...
- 131
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1
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194
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Implementation of mixed hybrid finite element method
The mixed hybrid finite element method (MHFEM) is based on the mixed finite element method (MFEM). So, I'd recall the implementation of MFEM.
The mixed formulation of Poisson equation reads
$$\begin{...
- 323
3
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1
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305
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Comparison on adaptive mesh refinement on finite elements and finite differences
My current work requires using (Adaptive Mesh Refinement) AMR to resolve multi scale physics. I have a general question whether finite element is better than finite difference in this aspect or not.
I ...
- 119
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241
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How to apply Neumann boundary conditions in Newton's method [closed]
Suppose that I have a very long and tedious set of differential equations. After discretization, I can get a mapping $f:\mathbb{R}^N \to \mathbb{R}^N$ such that solutions $\phi =(\phi_0,...,\phi_{N-1})...
- 111
3
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89
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Instability at the boundary of a finite difference simulation of a hyperbolic PDE
I want to simulate the hyperbolic partial differential equation
$$W_{tt} + V W_{tx} + k_E V W_x + k W_t = 0,$$
but I am having trouble finding a discrete analog of this equation which is numerically ...
- 131
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1
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106
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How to decrease error in (FTCS) forward time centered space method?
I am using the FTCS method for solving differential equations. I know that the condition for stable output is
$$
\frac{\alpha \Delta t}{\Delta x ^2} < \frac{1}{2}
$$
But when I use the distance ...
- 13
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1
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208
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Technique to find the CFL condition using the Galerkin method in space and finite-difference in time?
I am using the Galerkin method (Discontinuous to be precise) to discretize in space the scalar linear wave equation and the explicit second order centered finite difference scheme to discretize in ...
- 155
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4
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698
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Finite-difference software for solving custom equations
Are there any good, easy to use, software for simulating the evolution of systems of generic differential equations? I know there are custom programs for various specific circumstances (such as ...
- 201
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2
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269
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$P0$ elements for $H1$
Are there $P0$ (zero degree/constant element) nonconforming methods for approximating solutions in $H1$? More specifically, I have the equation:
$$u-f - T\Delta u = 0$$
Which can be interpreted as ...
- 2,267