## Applied **Mathematics**

Mathematics with a side of Engineering and Physics.

## Current Research

Finite Element Methods in Solid Mechanics

Computational Biomechanics of Skeletal Muscle

Numerical Analysis of Partial Differential Equations

Spectral Methods for Pseudodifferential Operators

## Publications

- J.A. Almonacid and N. Nigam.
*Characterization of singular flows of zeroth-order pseudo-differential operators via elliptic eigenfunctions: a numerical study.*arXiv e-prints, arXiv:2210.13622 (2022). Submitted. - J.A. Almonacid, S.A. Dominguez-Rivera, R.N. Konno, N. Nigam, S.A. Ross, C. Tam, and J.M. Wakeling.
*A three-dimensional model of skeletal muscle tissues.*arXiv e-prints, arXiv:2207.02421 (2022). Submitted. - J.A. Almonacid, H. Díaz, G.N. Gatica and A. Márquez.
*A fully-mixed finite element method for the coupling of the Stokes and Darcy-Forchheimer problems.*IMA J. Numer. Anal. 40 (2020), no. 2, 1454-1502. - J.A. Almonacid, G.N. Gatica, R. Oyarzúa and R. Ruiz-Baier.
*A new mixed finite element method for the n-dimensional Boussinesq problem with temperature-dependent viscosity.*Netw. Heterog. Media (2020). https://doi.org/10.3934/nhm.2020010 - J.A. Almonacid and G.N. Gatica.
*A fully-mixed finite element method for the n-dimensional Boussinesq problem with temperature-dependent parameters.*Comput. Meth. Appl. Math. 20 (2020), no. 2, 187-213. - J.A. Almonacid, G.N. Gatica and R. Ruiz-Baier.
*Ultra-weak symmetry of stress for augmented mixed finite element formulations in continuum mechanics.*Calcolo 57 (2020), Art. 2. https://doi.org/10.1007/s10092-019-0351-2. - J.A. Almonacid, G.N. Gatica and R. Oyarzúa.
*A posteriori error analysis of a mixed-primal finite element method for the Boussinesq problem with temperature-dependent viscosity.*J. Sci. Comput. 78 (2019), no. 2, 887-917. Full-text view-only version: https://rdcu.be/4YAs. - J.A. Almonacid, G.N. Gatica and R. Oyarzúa.
*A mixed-primal finite element method for the Boussinesq problem with temperature-dependent viscosity.*Calcolo 55 (2018), no. 3, Art. 36, 42 pp. Full-text view-only version: https://rdcu.be/32pk.

### Theses

*Internal Wave Attractors and Spectra of Zeroth-order Pseudo-Differential Operators.* Supervisors: Nilima Nigam and Weiran Sun. In partial fullfillment of the requirements for the degree of Master of Science in Applied and Computational Mathematics, Department of Mathematics, Simon Fraser University (2020). [Thesis PDF][Defence Slides][Github]

*Numerical Analysis of a Mixed Finite Element Method for the Boussinesq Problem with Temperature-Dependent Viscosity.* Supervisors: Gabriel N. Gatica and Ricardo E. Oyarzúa. In partial fullfillment of the requirements for the professional title of "Mathematical Civil Engineer", Faculty of Physical and Mathematical Sciences, Universidad de Concepción (2017). [PDF]

## Talks

*Finite-element discretization of a 3D hyperelastic model of skeletal muscle*, at 2022 CMS Winter Meeting, Toronto, Canada. Co-authors: Neuromuscular Mechanics Laboratory (SFU).*Turbulence in the air: from data points to a heat map (an IPSW problem)*, at Grad SOCIAL Seminar Series, Department of Mathematics, Simon Fraser University, 2022.*Singular solutions and the spectrum of a zeroth-order pseudo-differential operator*, at Cascade RAIN Meeting 2020. Virtual Conference. Co-authors: Nilima Nigam (SFU) and Maciej Zworski (UC Berkeley).[PDF]*Attractors and the spectrum of a zeroth-order pseudo-differential operator*, at Miniconference on Sharp Eigenvalue Estimates for Partial Differential Operators (in lieu of the AMS Spring Sectional Meeting 2020, West Lafayette, IN, United States). Virtual Conference. Co-authors: Nilima Nigam (SFU) and Maciej Zworski (UC Berkeley).[PDF]*A posteriori error analysis of a mixed finite element method for nonisothermal flow*, at CAIMS Annual Meeting 2019, Whistler, BC, Canada. Co-authors: Gabriel N. Gatica (UdeC) and Ricardo Oyarzua (UBB).*Mixed finite element methods for natural convection problems with nonconstant physical properties,*at Young Researchers in Mathematics YRM2018, Southampton, United Kingdom. Co-authors: Gabriel N. Gatica (UdeC), Ricardo E. Oyarzúa (UBB) and Ricardo Ruiz Baier (Oxford).*A priori error analysis of a mixed-primal formulation for the Boussinesq problem with temperature-dependent viscosity,*at XXVI Congreso de Matemática Capricornio COMCA-2017, Arica, Chile. Co-authors: Gabriel N. Gatica (UdeC), Ricardo E. Oyarzúa (UBB).- Research visits experience at SFU:
*Towards a valid approximation for the Neutron Transport Equation using Regularized Classical Half-Space Equations over the 2D unit disk,*at Seminario de Análisis Numérico y Modelación Matemática (GIMNAP-UBB & CI²MA), Concepción, Chile. Co-authors: Weiran Sun (SFU).

### Mini-symposia Organization

- Advances in Finite Elements & Applications to Fluid and Solid Mechanics, at 2022 CMS Winter Meeting. Joint organization with Nilima Nigam (SFU).

### Other Attended Conferences

- Numerical Methods for Spectral Problems NMSP2019, Research Institute for the Mathematical Sciences, Kyoto University, Kyoto, Japan.
- Ninth Meeting on Numerical Analysis of Partial Differential Equations "Santiago Numérico III", 2017, Pontificia Universidad Catolica de Chile, Santiago, Chile.
- Fifth Chilean Workshop on Numerical Analysis of Partial Differential Equations WONAPDE 2016, Universidad de Concepcion, Concepción, Chile.

## Posters

*A parallel finite element solver for hyperelastic deformations*, at Third Biennial Meeting of SIAM Pacific Northwest Section 2022, Vancouver, WA, United States.*High-order discretizations of a linear forced wave equation*(Best Poster Award), at Second Biennial Meeting of SIAM Pacific Northwest Section 2019, Seattle, WA, United States. Co-authors: Nilima Nigam. [PDF]

## Industrial Problem Solving Workshops (IPSWs)

*Turbulence in the air: creating a heat map and building a seasonal diagram.*Presented by the International Air Transport Association (IATA) at the 12th Montreal Industrial Problem Solving Workshop, August 22-26, 2022, Montreal, QC, Canada. [Initial Presentation] [Final Presentation]

## About Me

Right after finishing high school in Puerto Natales (Patagonia, Chile) I moved north to Concepción (Bío Bío) to begin my undergraduate studies at Universidad de Concepción in the field of Applied Mathematics. After 6 (+ε) years, on August 2017, I defended my thesis on the analysis of a mixed finite element method for the equations modelling heat transfer processes via natural convection for variable-viscosity fluids (supervised by Gabriel N. Gatica and Ricardo E. Oyarzúa). This allowed me to obtain the professional title of "Mathematical Civil Engineer". Later, I worked as a Research Assistant at the Center for Research in Mathematical Engineering (CI²MA) in Concepción, to then move further north to begin graduate studies in Applied and Computational Mathematics in the Department of Mathematics at Simon Fraser University (Vancouver, BC, Canada).

## Contact

# javiera [at] sfu [dot] ca

**Department of Mathematics**

Simon Fraser University

8888 University Drive

Burnaby, BC V5A 1S6

Canada