Vilhelm's homepage

GAMM-ANLA meeting 2025

Thu, 02 Oct 2025 22:23:52 +0200

I will be at this year’s GAMM-ANLA meeting. It is the 25th annual ANLA-meeting, and this year it is taking place in Bologna, Italy. I am very excited to attend this year, and I will be presenting results from the recent preprint From eigenvector nonlinearities with quadratic structure to eigenvalue nonlinearities with algebraic structure in the form of a talk. See you there!

Teacher of the year 2025

Mon, 15 Sep 2025 22:16:13 +0200

Thank you very, very much to the students of the T-section (sw. Farkostteknik) at KTH for awarding me ‘’teacher of the year 2025’’! Teaching differential equations to all of you over the past four years have been so much fun, and I have learnt more from you than I had ever expected. Thank you for all the encouragement, and I hope to see you soon at KTH!

Motivation (Swedish only)

Vilhelm har under flera år hjälpt T-teknologer igenom Diff-kursen och varit en väldigt uppskattad övningsassistent. Han är duktig på att identifiera svåra koncept och kan förklara dessa på ett pedagogiskt och lättförståeligt sätt. Vilhelm fångar klassen med sitt lättsamma sätt att undervisa samtidigt som han kompletterar föreläsningarna och ökar förståelse för kursens innehåll. Därför tilldelas Vilhelm Peterson Lithell utmärkelsen Årets Lärare 2025.

Nordic NLA meeting 2025

Sat, 26 Jul 2025 12:39:43 +0200

This year’s Nordic NLA meeting will be held in Uppsala, Sweden, and I will be attending. The workshop is organized during two days in August, the 19th-20th.

I will be presenting our results from the recent preprint From eigenvector nonlinearities to eigenvalue nonlinearities. Last year was a lot of fun, and I think this year’s meeting will be too.

New preprint online

Mon, 23 Jun 2025 17:55:16 +0200

My supervisor Elias Jarlebring and I just published a new preprint titled From eigenvector nonlinearities to eigenvalue nonlinearities to arXiv. We show how certain types of problems with eigenvector-nonlinearities can be transformed into equivalent problems with eigenvalue nonlinearities, a problem class that is much better understood. We can use established methods for these problems to compute solutions of the original problem. arXiv link.

I will be at BIT65

Wed, 18 Dec 2024 21:30:42 +0100

BIT Numerical Analysis is celebrating its 65:th anniversary with a three day conference on the 14:th-16:th of January, in Uppsala, Sweden. Link.

I will be holding a presentation on ongoing work with my supervisor. We are developing a new method for a particular class of nonlinear eigenvalue problems with eigenvector nonlinearities (NEPv), motivated by the Gross-Pitaevskii eigenvalue problem. You can find my abstract below.

Abstract: We study eigenvalue problems in which there is a nonlinear dependence on the eigenvector, abbreviated NEPv. In this sense, these problems generalize the familiar linear eigenvalue problem. Specifically, we consider nonlinearities that appear as a sum of products of scalar functions of the eigenvector, and rank-one matrices. The target problems may contain many such nonlinear terms. Our attention is focused on exploiting this and similar structures that appear for instance in the Gross-Pitaevskii equation. To this end we present a method for reformulating the class of problems of this form into equivalent problems with eigenvalue nonlinearities (NEP), enabling us to use efficient methods for these problems as a means of obtaining solutions to the NEPv. In particular, these methods can efficiently compute several eigenvalues. We show how the transformation from NEPv to NEP can be constructed theoretically, and indicate how it can be handled in practice. Numerical experiments demonstrate the effectiveness of our approach.