Jared Frazier

Jared Frazier

Scientific programmer at Leibniz Institute of Atmospheric Physics

Posts by Tags

gateaux derivative

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

22 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.

jacobian

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

22 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

22 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

22 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.

pdes

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

22 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.

petsc

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

22 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

22 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.