Publication

Testing Benchmark for a Block Conjugate Gradient Solving Scheme in Poroelasticity

2023
Student project
Abstract

With the advancement in fields of science more complex and more coupled phenomena can be explained, calculated and predicted. To solve these problems one has to update the related tools. Since analytical solutions do not exist for all physical processes, solving system of equation numerically has been a readily adopted and proven effective strategy. However, once a new solving strategy is developed, it must be checked for correctness. One way is to compare the output of the new method, to a known analytical solution. This is what this report is aiming to do. We will adopt the Block Conjugate Gradient solving method to a poroelastic Borehole Problem, which is a problem for which analytical solutions exist, to test the effectiveness of the solver.

About this result
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.
Ontological neighbourhood
Related concepts (33)
Euler method
In mathematics and computational science, the Euler method (also called the forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. It is the most basic explicit method for numerical integration of ordinary differential equations and is the simplest Runge–Kutta method. The Euler method is named after Leonhard Euler, who first proposed it in his book Institutionum calculi integralis (published 1768–1870).
Iterative method
In computational mathematics, an iterative method is a mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class of problems, in which the n-th approximation is derived from the previous ones. A specific implementation with termination criteria for a given iterative method like gradient descent, hill climbing, Newton's method, or quasi-Newton methods like BFGS, is an algorithm of the iterative method.
Numerical stability
In the mathematical subfield of numerical analysis, numerical stability is a generally desirable property of numerical algorithms. The precise definition of stability depends on the context. One is numerical linear algebra and the other is algorithms for solving ordinary and partial differential equations by discrete approximation. In numerical linear algebra, the principal concern is instabilities caused by proximity to singularities of various kinds, such as very small or nearly colliding eigenvalues.
Show more
Related publications (63)

On the fast assemblage of finite element matrices with application to nonlinear heat transfer problems

The finite element method is a well-established method for the numerical solution of partial differential equations (PDEs), both linear and nonlinear. However, the repeated re -assemblage of finite element matrices for nonlinear PDEs is frequently pointed ...
ELSEVIER SCIENCE INC2023

Method for Design Materialization (MDM) for artists, educators and archivists: an introduction. ISEA 2023.

This contribution argues for the potential of Barr, Khaled and Lessard’s Method for Design Materialization (MDM) as a research through design tool that is specifically suited for new media preservation. Building moreover from the ISEA first and second Summ ...
2023

Method for Design Materialization (MDM) for artists, educators and archivists: an introduction

This contribution argues for the potential of Barr, Khaled and Lessard’s Method for Design Materialization (MDM) as a research through design tool that is specifically suited for new media preservation. Building moreover from the ISEA first and second Summ ...
2023
Show more
Related MOOCs (18)
Warm-up for EPFL
Warmup EPFL est destiné aux nouvelles étudiantes et étudiants de l'EPFL.
Matlab & octave for beginners
Premiers pas dans MATLAB et Octave avec un regard vers le calcul scientifique
Matlab & octave for beginners
Premiers pas dans MATLAB et Octave avec un regard vers le calcul scientifique
Show more