Jared Frazier

Jared Frazier

Scientific Programmer at the Leibniz Institute of Atmospheric Physics

Posts by Tags

gateaux derivative

Extra Mathematical Details: The Steady-State Reaction-Diffusion Equation and its Solution in PETSc

23 minute read

Published:

In this article, some extra mathematical details related to the solution of the steady-state reaction-diffusion equation using PETSc are discussed. First, the simple nonlinear governing equation of interest is shown. Then, Newton’s method is presented at the partial differential equation (PDE) level for generality rather than being presented at the algebraic level. Subsequently, the spatial discretization via the finite difference method is shown for completeness. Finally, a commented PETSc implementation of the discretized reaction-diffusion equation is shown to concretely illustrate how the mathematical notation maps to code.

how-to

How-to: Enable nvim color schemes in tmux windows

3 minute read

Published:

I am constantly using ssh to remotely login to different compute clusters (e.g., DKRZ’s Levante, ECMWF’s Atos, local clusters at work, etc.). I find it much more convenient to use a terminal-based text editor like neovim coupled with the standard terminal multiplexer tmux in order to switch easily between several programs in one terminal. However, I quickly encountered an issue where my neovim color scheme was not displayed when using it within tmux. Fortunately, there’s an easy fix to this issue that I cover in this article. I first show the problem and the expected behavior, diagnose the error, and then correct it accordingly. I document the solution here and tie to use with legacy systems.

How-to: Update PDF Metadata Using pdftk

1 minute read

Published:

I often download and read scientific journal articles on my Kobo eReader. Unfortunately, the metadata in the PDFs for such journal articles may lack title information. This means that the searchable title that appears for the article once loaded onto the eReader is something very ugly like an uninterpretable string of digits. An easy way to fix this is using the open-source tool pdftk. In this short article, I show how to use pdftk for this purpose.

jacobian

Extra Mathematical Details: The Steady-State Reaction-Diffusion Equation and its Solution in PETSc

23 minute read

Published:

In this article, some extra mathematical details related to the solution of the steady-state reaction-diffusion equation using PETSc are discussed. First, the simple nonlinear governing equation of interest is shown. Then, Newton’s method is presented at the partial differential equation (PDE) level for generality rather than being presented at the algebraic level. Subsequently, the spatial discretization via the finite difference method is shown for completeness. Finally, a commented PETSc implementation of the discretized reaction-diffusion equation is shown to concretely illustrate how the mathematical notation maps to code.

newton's method

Extra Mathematical Details: The Steady-State Reaction-Diffusion Equation and its Solution in PETSc

23 minute read

Published:

In this article, some extra mathematical details related to the solution of the steady-state reaction-diffusion equation using PETSc are discussed. First, the simple nonlinear governing equation of interest is shown. Then, Newton’s method is presented at the partial differential equation (PDE) level for generality rather than being presented at the algebraic level. Subsequently, the spatial discretization via the finite difference method is shown for completeness. Finally, a commented PETSc implementation of the discretized reaction-diffusion equation is shown to concretely illustrate how the mathematical notation maps to code.

nonlinear

Extra Mathematical Details: The Steady-State Reaction-Diffusion Equation and its Solution in PETSc

23 minute read

Published:

In this article, some extra mathematical details related to the solution of the steady-state reaction-diffusion equation using PETSc are discussed. First, the simple nonlinear governing equation of interest is shown. Then, Newton’s method is presented at the partial differential equation (PDE) level for generality rather than being presented at the algebraic level. Subsequently, the spatial discretization via the finite difference method is shown for completeness. Finally, a commented PETSc implementation of the discretized reaction-diffusion equation is shown to concretely illustrate how the mathematical notation maps to code.

nvim

How-to: Enable nvim color schemes in tmux windows

3 minute read

Published:

I am constantly using ssh to remotely login to different compute clusters (e.g., DKRZ’s Levante, ECMWF’s Atos, local clusters at work, etc.). I find it much more convenient to use a terminal-based text editor like neovim coupled with the standard terminal multiplexer tmux in order to switch easily between several programs in one terminal. However, I quickly encountered an issue where my neovim color scheme was not displayed when using it within tmux. Fortunately, there’s an easy fix to this issue that I cover in this article. I first show the problem and the expected behavior, diagnose the error, and then correct it accordingly. I document the solution here and tie to use with legacy systems.

pdes

Extra Mathematical Details: The Steady-State Reaction-Diffusion Equation and its Solution in PETSc

23 minute read

Published:

In this article, some extra mathematical details related to the solution of the steady-state reaction-diffusion equation using PETSc are discussed. First, the simple nonlinear governing equation of interest is shown. Then, Newton’s method is presented at the partial differential equation (PDE) level for generality rather than being presented at the algebraic level. Subsequently, the spatial discretization via the finite difference method is shown for completeness. Finally, a commented PETSc implementation of the discretized reaction-diffusion equation is shown to concretely illustrate how the mathematical notation maps to code.

pdf

How-to: Update PDF Metadata Using pdftk

1 minute read

Published:

I often download and read scientific journal articles on my Kobo eReader. Unfortunately, the metadata in the PDFs for such journal articles may lack title information. This means that the searchable title that appears for the article once loaded onto the eReader is something very ugly like an uninterpretable string of digits. An easy way to fix this is using the open-source tool pdftk. In this short article, I show how to use pdftk for this purpose.

pdftk

How-to: Update PDF Metadata Using pdftk

1 minute read

Published:

I often download and read scientific journal articles on my Kobo eReader. Unfortunately, the metadata in the PDFs for such journal articles may lack title information. This means that the searchable title that appears for the article once loaded onto the eReader is something very ugly like an uninterpretable string of digits. An easy way to fix this is using the open-source tool pdftk. In this short article, I show how to use pdftk for this purpose.

petsc

Extra Mathematical Details: The Steady-State Reaction-Diffusion Equation and its Solution in PETSc

23 minute read

Published:

In this article, some extra mathematical details related to the solution of the steady-state reaction-diffusion equation using PETSc are discussed. First, the simple nonlinear governing equation of interest is shown. Then, Newton’s method is presented at the partial differential equation (PDE) level for generality rather than being presented at the algebraic level. Subsequently, the spatial discretization via the finite difference method is shown for completeness. Finally, a commented PETSc implementation of the discretized reaction-diffusion equation is shown to concretely illustrate how the mathematical notation maps to code.

time independent

Extra Mathematical Details: The Steady-State Reaction-Diffusion Equation and its Solution in PETSc

23 minute read

Published:

In this article, some extra mathematical details related to the solution of the steady-state reaction-diffusion equation using PETSc are discussed. First, the simple nonlinear governing equation of interest is shown. Then, Newton’s method is presented at the partial differential equation (PDE) level for generality rather than being presented at the algebraic level. Subsequently, the spatial discretization via the finite difference method is shown for completeness. Finally, a commented PETSc implementation of the discretized reaction-diffusion equation is shown to concretely illustrate how the mathematical notation maps to code.

tmux

How-to: Enable nvim color schemes in tmux windows

3 minute read

Published:

I am constantly using ssh to remotely login to different compute clusters (e.g., DKRZ’s Levante, ECMWF’s Atos, local clusters at work, etc.). I find it much more convenient to use a terminal-based text editor like neovim coupled with the standard terminal multiplexer tmux in order to switch easily between several programs in one terminal. However, I quickly encountered an issue where my neovim color scheme was not displayed when using it within tmux. Fortunately, there’s an easy fix to this issue that I cover in this article. I first show the problem and the expected behavior, diagnose the error, and then correct it accordingly. I document the solution here and tie to use with legacy systems.